













A POCKET-BOOK 

OF 

MECHANICAL ENGINEERING 


TABLES, DATA, FORMULAS, THEORY 
AND EXAMPLES 


FOR ENGINEERS AND STUDENTS 


BY 


CHARLES M. SANIES, B.Sc. 

Mechanical Engineer 


THIRD EDITION, REVISED AND ENLARGED 
THIKD THOUSAND 


( 

If# 


JERSEY CITY, N. J. 

CHARLES M. SAMES 

1908 



« 


LIBRARY of CONGRESS 

Two G-joles, Received 

nov % 


Cepvnarht Entry 


BSi* 


e/^/ 

XXc,,No, 


/q( s 

COPY B. 


Copyright, 1905, 1906, 1907, 

BY 

CHARLES M. SAMES 



ROBERT DRUMMOND COMPANY, PRINTERS, NEW YORK 








PREFACE. 


This book is the result of the writer’s endeavor to compact the greater 
part of the reference information usually required by mechanical engi¬ 
neers and students into a volume whose dimensions permit of its being 
carried in the pocket without inconvenience. 

In its preparation he has consulted standard treatises and reference 
books, the transactions of engineering societies, and his own memoranda- 
which extend back over a period of fifteen years. A large amount of val¬ 
uable and timely matter has been obtained from the columns of technical 
periodicals and also from the catalogues which manufacturers have cour¬ 
teously placed at his disposition. 

While very great care has been taken in the preparation of manuscript 
and in the reading of proofs, it is nevertheless a regrettable fact that 
first editions are not always infallible, and the writer will accordingly be 
under obligations to those who will call his attention to such errors in 
statement or typography as may come to their notice. 

Suggestions indicating how subsequent editions may be made of greater 
usefulness are respectfully solicited. 

Charles M. Sames. 



SECOND EDITION, FOR 1907. 


All matter contained in the first edition has been carefully scrutinized 
for errors, comparisons having been made with the original sources of the 
information from which it was compiled, as it was found that nearly all 
the inaccuracies occurred through recopying from notes. 

A number of alterations have been made in the text, certain data have 
been replaced by fresher matter, and the work has been enlarged by the 
addition of an appendix in which new subjects are treated, some omis¬ 
sions supplied, and much space given to recent and valuable matter relat¬ 
ing particularly to Machine Design. 


Ill 


C. M. S. 




IV 


PREFACE. 


THIRD EDITION, FOR 1908. 


New matter has been added on a number of subjects, including those of 
D, -in forced Concrete, High-speed Tool Steel, Superheated Steam and Journal 
1 iction. A few changes have also been made in the text, in order to bring 
• „ down to the date of publication. 


C. M. S. 


CONTENTS 


• PAGE 

MATHEMATICS. , 

Weights anti Measures. Arithmetic. Algebra. Logarithms. 
Mensuration. Trigonometry. 


CHEMICAL DATA. . ..‘.. 10 

MATERIALS. 11 


Properties and Tables of Weights of Metals, Woods, Stones and 
Building Materials. Weights and Dimensions of Rods, Bars, 
Pipes, Boiler Tubes, Bolts, Nuts, Rivets, Nails, Screws, 
Wire-Rope, Chains, etc. 

THE STRENGTH OF MATERIALS, STRUCTURES, AND 

MACHINE PARTS. 18 

Stresses. Strength of Materials. Factors of Safety. Strength 
of Chains, Ropes, Cylinders, Boilers, Bolts, Fly-wheels, Riveted 
Joints, Cotter Joints, Shafting, Keys, Springs, Beams, Flat Plates, 
Stayed Surfaces, Crane Hooks, Columns and Struts, etc. Car¬ 
negie Steel Tables. Reinforced Concrete. Graphic Statics. Stress 
Diagrams for Framed Structures, etc. 

ENERGY AND THE TRANSMISSION OF POWER. 43 

Force. Mass. Energy. Power. Elements of Machines. Ma¬ 
chine Parts. Connecting-Rods. Shafting. Journals. Ball and 
Roller-Bearings. Gearing. Belting. Pulleys. Rope Transmis¬ 
sion. Friction. Lubrication. Power Measurement, etc 

HEAT AND THE STEAM ENGINE. 56 

Heat. Steam. Thermal Efficiencies. Indicator Diagrams. 
Engine Design and Data. Temperature-Entropy Diagrams. 
Steam Turbines. Locomotives. Steam Boilers and Accessory 
Apparatus. Internal-Combustion Engines. Air. Compressed 
Air. Fans and Blowers. Heating and Ventilation. Mechanical 


Refrigeration, etc. 

HYDRAULICS AND HYDRAULIC MACHINERY. 106 

Hydraulics. Water Wheels. Turbines. Pumps. Plunger 


Pumps and Pumping Machinery. Hydraulic Power-TransmiS' 
sion, etc. 


V 










vi 


CONTENTS. 


PAGE 

SHOP DATA... 117 

Cupola Data. Welding. Tempering. Screw Threads. Wire 
and Sheet-Metal Gauges. Fits. Grinding Wheels and Data. 
Cutting Speeds. High-Speed Tool Steel. Power Required by 
Machinery. Cost of Power and Power Plants, etc. 

ELECTROTECHNICS.:. 130 

Electric Currents. Electro-Magnetism. Electro-Magnets. CoL- 
tinuous-Current Dynamos and Motors. Alternating Currents. 
Alternating-Current Generators. Transformers. Electric Power 
Transmission. Electric Lighting. Electric Traction, etc. 

APPENDIX.. 162 












SYMBOLS AND ABBREVIATIONS 


A 

Am. Mach. 
a 

Bm 

B.H.P. 

B. T. 
B.T.U. 

B. W.G. 

C. 

C 

C. I. 
c. 

cm. 

c :g- .. 

cir. mils 
c.-p. 
cu. 
coeff. 

D 

d 

degs. 

E 

E.H.P. 

E.M.F. 

E. N. 

E. R. 

E. W. & E. 

F. 

Fn 

f 

fc, fSi ft 


ft.-lbs. 

G 

Q 

gal. 

g-cal. 

II 


Area in square feet. 

American Machinist. 

Area in square inches. 

Bending moment. 

Brake horse-power. 

Board of Trade. 

British thermal unit. 

Birmingham wire gauge. 

Centigrade. 

Modulus of transverse elasticity. 

Cast iron. 

Center. 

Centimeters. 

Center of gravity. 

Circular mils. 

Candle-power. 

Cubic. 

Coefficient. 

Larger, or outside, diameter in inches. 

Diameter in inches (diam.). 

Degrees. 

Modulus of direct elasticity. 

Electrical horse-power. 

Electro-motive force. 

Engineering News. 

Engineering Record. 

Electrical World and Engineer. 

Fahrenheit. 

Tractive force in pounds. 

Acceleration in feet per second. 

Stresses in pounds per square inch (compression, shear, ten¬ 
sion). 

Modulus of rupture. 

Feet. 

Foot-pounds. 

Pounds in one cubic foot of water. 

Acceleration of gravity in feet per second ( = 32.16); Grams, 
Gallons. 

Gram-calories. 

Height or head in feet; total heat in steam above 32° F., in 
B.T.U. 


H. P. Rated horse-power. 

h Height in inches; sensible heat in the liquid above 32° F. 

hor. Horizontal, 

hr. Hours. 

I Moment of inertia. 

I r Polar moment of inertia. 

I. H.P. Indicated horse-power. 

Ing. Taschenbuch. Engineer’s Pocket Book (Hiitte), Berlin, 
in. Inches. 


Vll 



yin 


K 

kv 

kp 

kg. 

km. 

kw. 

L 

l 

lb. 

lin. 

M 

M.E.P. 

M.M.F. 

m 

m. 

mm. 

m.-kg. 

N 

n 

P 

V 

v" 

pm 

perp. 

Q 

Q 

R 

r 


r.p.m. 

S 
S t 
s 

sec. 

sp. gr. 

sq. 

T 

T m 
Tn 
t 

t° (or f) 
tn 

V 

v 

vert. 

W. I. 

w 

D. T. 

a (Alpha) 

/? (Beta) 
r (Gamma) 
A (Delta) 

5 “ 'l 


SYMBOLS AND ABBREVIATIONS. 


t) (Eta) 

0 (Theta) 
n Mu) 

* (Pi) 

p (Rho) 

I (Sigma) 
r (Tau) 

4> (Phi) 

oC 

> 

< 

'll 

+ 


Modulus of volumetric elasticity. 

Specific heat at constant volume. 

1 . i «* “ “ pressure. 

Kilograms; kg.-m., kilogram-meters. 

Kilometers. 

JSngThta'feet; latent heat in B.T.U. per lb. of steam. 

Length in inches. 

Pounds. 

Linear. 

Poisson’s ratio. 

See pm. . 

Magneto-motive force. 

Mass in pounds = w-i-g. 

Meters. 

Millimeters. 

Meter-kilograms. , . 

Number of revolutions per minute. 

.. • * “ “ second. 

Total pressure in pounds. . , 

Pressure, in pounds per square inch. 

Mean ’elective pressure' £ pounds per square inch. 

FtoTof Sror’water in cubic feet per minute. 

l^S^Se^SS^yS^'inches; ratio of 

pansion. 

Revolutions per minute. 

Modulus of section in bending. 

SiJof square in «" 

Seconds. 

Specific gravity. 

Absolute temperature in degs. F. (also r). 

Twisting moment. 

Greater tension m belt or rope. 

Thickness in inches; time in seconds. 

Temperature, or rise of temperature in degs. . 

T<psspr tension in belt or i opc« . i • r i 

Velocity in feet per minute; volume in cubic feet. 

Velocity in feet per second. 

Vertical. 

Wrought iron. . . 

Weight or load in pounds (also wt.;. 

ZeTtschrift des Vereines deutscher Ingcnieure. Berlin. 
Coefficient of linear expansion in degs. I., an ang e. 

An angle. . 

Pitch angle in spiral gears. , . , 

«’ s1faTn a p” e mch of length (due to com- 
C> ’ pression, laterally, shear, and tension, respecti\ely). 
Efficiency. 

Coefficient of friction; tangent of fnctionangle. 

Ratio of circumference to diameter — 3.141by +. 

Radius of curvature in bending. 

ttU mmSSrS'F.; normal pitch in spiral gears. 

Entropy. 

“Varies as. 

Greater than. 

Less than. 

Parallel to. 

Across. 


MATHEMATICS. 


"WEIGHTS AND MEASURES (ENGLISH). 

t oncrtVi 1 000 mils = 1 inch; 12 inches = 1 foot; 3 feet — 1 yard; 5.5 
Length. l.OUU h . j 92 inches = 1 link; 100 links =1 chain; 

80 chains ilmile = 5,280 feet! 1 furlong = 40 rods; 1 knot or nautical mile 

= 6,080.26 feet = i league. j . qn “^5 so vd = lsq. 


= 1 pull/. & pinto— A quai w » * m 441 * . . “ - 

loll (tJ s. gal. = 231 CU. in.; British Imperial gal. = 277.274 cu. m ); o 

60 minims-1 fluid drachm; 8 
drachms = 1 fluid ounce = 437.o f™m s . auarts = l peck; 4 pecks = 

1 bmher-2 a i50.42 m - ,.m - /W cudt. (l'British bushel-8 Imperial gal. 
- 2 cfrcu.a 2 r Kur^^oVseconds-l minute; 60 minutes-1 degree; 90 

*RK 'deasure 1 (lit WBiTno."'' feet board measure - length in feet X 
width in feet X thickness in inches. 

METRIC MEASURES. 

Myria= 10,000. Q 070113 in =3.28084 ft. 1 kilometer = 3,280.843 

Length. 1 meter-39.3701 10 • , =2 5A millimeters. 1 

ft. =0.02137 mile. 1 ^nch-^.o4 centime . tern ^ 1609.3 meters. 

2°47lt Acres'.' 1 Sre - 0.4047 hect«|. 1 sq- mile-259 hectares. 1 sq. 

ft. = 0 092903 sq. m. V^/u'+ir-lcn meter = 35 3148 cu. ft. 1 liter (1.) 

(D. S.). 1 gal. CU. 80- 

"'WeighT 1 1 g}am° m (or ££ = 

2.20462 lb. avoirdupois. 1 metric ton i,u 

0.0648 gram. 1 Tib per sq. in. = 0.070308 kg. per sq. cm. 

Pressure and Weight. 1 lb - P . metric atmosphere. 1 atmos- 

1 kg. per sq. cm. = 14.223 Jb. pe q ft . = 33.947 ft. of water = 

phere (14.7 lb. P e . r mm Vat ’ 62° F 1 lb. per sq. in. = 27.71 m, of water 

30 in. of mercury (762 mm.) at w r. 1 H 

= 2.0416 in. of mercury at 62 £. 



n 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 


MATHEMATICS 


ARITHMETIC AND ALGEBRA. 

Cubes of Numbers. Circumferences and Areas of 
Circles. 


n 2 

n 3 

Tin 

;rn 2 -7-4 

1 

1 

3.142 

0.7854 

4 

8 

6.283 

3.1416 

9 

27 

9.425 

7.0686 

16 

64 

12.566 

12.5664 

25 

125 

15.708 

19.6350 

36 

216 

18.850 

28.2743 

49 

343 

21.991 

38.4845 

64 

512 

25.133 

50.2655 

• 81 

729 

28.274 

63.6173 

100 

1000 

31.416 

78.5398 

121 

1331 

34.558 

95.0332 

144 

1728 

37.699 

113.097 

169 

2197 

40.841 

132.732 

196 

2744 

43.982 

153.938 

225 

3375 

47.124 

176.715 

256 

4096 

50.265 

201.062 

289 

4913 

53.407 

226.980 

324 

5832 

56.549 

254.469 

361 

6859 

59.690 

283.529 

400 

8000 

62.832 

314.159 

441 

9261 

65.973 

346.361 

484 

10648 

69.115 

380.133 

529 

12167 

72.257 

415.476 

576 

13824 

75.398 

452.389 

625 

15625 

78.540 

490.874 

676 

17576 

81.681 

530.929 

729 

19683 

84.823 

572.555 

784 

21952 

87.965 

615.752 

841 

24389 

91.106 

660.520 

900 

27000 

94.248 

706.858 

961 

29791 

97.389 

754.768 

1024 

32768 

100.531 

804.248 

1089 

35937 

103.673 

855.299 

1156 

39304 

106.814 

907.920 

1225 

42875 

109.956 

962.113 

1296 

46656 

113.097 

1017.88 

1369 

50653 

116.239 

1075.21 

1444 

54872 

119.381 

1134.11 

1521 

59319 

122.522 

1194.59 

1600 

64000 

125.66 

1256.64 

1681 

68921 

128.81 

1320.25 

1764 

74088 

131.95 

1385.44 

1849 

79507 

135.09 

1452.20 

1936 

85184 

138.23 

1520.53 

2025 

91125 

141.37 

1590.43 

2116 

97336 

144.51 

1661.90 

2209 

103823 

147.65 

1734.94 

2304 

110592 

150.80 

1809.56 

2401 

117649 

153.94 

1885.74 

2500 

125000 

157.08 

1963.50 

2601 

132651 

160.22 

2042.82 

2704 

140608 

163.36 

2123.72 

2809 

148877 

166.50 

2206.18 

2916 

157464 

169.65 

2290.22 

3025 

166375 

172.79 

2375.83 

3136 

175616 

175.93 

2463.01 

3249 

185193 

179.07 

2551.76 

3364 

195112 

182.21 

2642.08 




















ARITHMETIC AND ALGEBRA 


3 


Squares and Cubes of Numbers. Circumferences and Areas of 

Circles. 


n 

n 2 

n 3 

Tin 

7 m 2 -5- 4 

59 

3481 

205379 

185.35 

2733.97 

60 

3600 

216000 

188.50 

2827.43 

61 

3721 

226981 

191.64 

2922.47 

62 

3844 

238328 

194.78 

3019.07 

63 

3969 

250047 

197.92 

3117.25 

64 

4096 

262144 

201.06 

3216.99 

65 

4225 

274625 

204.20 

3318.33 

66 

4356 

287496 

207.35 

3421.19 

67 

4489 

300763 

210.49 

3525.65 

68 

4624 

314432 

213.63 

3631.68 

69 

4761 

328509 

216.77 

3739.28 

70 

4900 

343000 

219.91 

3848.45 

71 

5041 

357911 

223.05 

3959.19 

72 

5184 

373248 

226.19 

4071.50 

73 

5329 

389017 

229.34 

4185.39 

74 

5476 

405224 

232.48 

4300.84 

75 

5625 

421875 

235.62 

4417.86 

76 

5776 

438976 

238.76 

4536.46 

77 

5929 

456533 

241.90 

4656.63 

78 

6084 

474552 

245.04 

4778.36 

79 

6241 

493039 

248.19 

4901.67 

80 

6400 

512000 

251.33 

5026.55 

81 

6561 

531441 

254.47 

5153.00 

82 

6724 

551368 

257.61 

5281.02 

83 

6889 

571787 

260.75 

5410.61 

84 

7056 

592704 

263.89 

5541.77 

85 

7225 

614125 

267.04 

5674.50 

86 

7396 

636056 

270.18 

5808.80 

87 

7569 

658503 

273.32 

5944.68 

88 

7744 

681472 

276.46 

6082.12 

89 

7921 

704969 

279.60 

6221.14 

90 

' 8100 

729000 

282.74 

6361.73 

91 

8281 

753571 

285.88 

6503.88 

92 

8464 

778688 

289.03 

6647.61 

93 

8649 

804357 

292.17 

6792.91 

94 

8836 

830584 

295.31 

6939.78 

95 

9025 

857375 

298.45 

7088.22 

96 

9216 

884736 

301.59 

7238.23 

97 

9409 

912673 

304.73 

7389.81 

98 

9604 

941192 

307.88 

7542.96 

99 

9801 

970299 

311.02 

7697.69 

100 

10000 

1000000 

314.16 

7853.98 


Square and Cube Root by Approximation. From above table take 
n whose cube or square is nearest the number of which the root is desired. 
For square root, divide the number by n, obtaining the quotient n \; take 
(n + «i)- 7-2 (=«- 2 )~for a new divisor, obtaining n 3 as a quotient; take 
( n 2 -I-n 3 )2 for a new divisor and continue process until divisor and quo¬ 
tient are alike, or to the required accuracy. 

For cube root, divide the number by n 2 , obtaining quotient^,; take 

(— l ^ ^ = n 2 2 for a new divisor, obtaining quotient n 3 ; take ( 

for a new divisor and continue process until (2nx + nx-\-\) 3 = quotient. 

Compound Interest. a = c(l + p) n , where a = amount, c = initial capi¬ 
tal, p = rate per cent in hundredths, and n — number of years. 

Binomial Theorem. 


(a±6) n = a n ±na n ! 5-f 


, n(n-l) _ _ , n(n — l)(n —2) 


1.2 


a n 2 b 2 ± 


a” 3 5 3 + 


1.2.3 

























4 


MATHEMATICS 


Arithmetical and Geometrical Progression. Let a = first term of 

the series, 6 = last term, d = difference between any two adjacent terms (in 
Arith. Prog.), n = number of terms, s = sum of all the terms, r = ratio of any 
term divided by preceding one (in Geom. Prog.). Then, for Arithmetical 

2s 

series, b = a + (n — 1)<2 =- a; 


71 r . , , ,, 6 "1” a 6" .. , v 71 71 roi / 1 \ ii 

s = —[2a + (n. — 1 )d] =* —^—h — 2d " = ^~ba)— ( n 


For Geometrical series, b = ar n x = 


a + 0—l)s (r — l)sr n 1 


a(r n — 1) r b — a b(r n — 1) 

r—1 r—1 (r— l)r" — 1 



. . log& — loga. 
n = H— , 

log r 


Sinking Fund for Depreciation and Renewal, s = a(r n — 1)-f-(r — 1), 

where s is the lund or amount to be accumulated in n years, and r = 1 plus 
the rate per cent of interest to be compounded annually, the rate being 
expressed in hundredths. Example. A certain machine costing $1,000 (s) 
will need to be replaced by a new one costing the same amount at the end 
of 10 years ( n ). What sum must be paid into a sinking fund at the end 
of each year to amount to $1,000 at the end of the tenth year, interest 
being compounded at the rate of 5 per cent? 1,000 = a(1.05 10 — 1) -s- (1.05 — 1), 
and a, or the annual amount to be placed in the fund, =$79.50. 

Interpolation. Where a value intermediate to two values in a table is 
desired, the following formula may be employed. Value desired, 


. , . n(n— l)c , n(n— l)(n — 2)d 

a x — a + nb+ l72 — + --+ 


Let N, N i, N 2 and Ns be four numbers (equally spaced) whose tabular 
functions are a, ai, a 2 and a 3 . Then, in above formula to find a x , the tabu¬ 
lar function of N x (lying between N and Ni), n = ~ — zr T . 

iVi — iV 

5 = the first of the first order of differences, 

c= “ “ “ “ second “ “ 

d= “ “ “ “ third “ “ “ , etc. 

Example. The chords of 30°, 32°, 34° and 36° are 0.5176, 0.5513, 0.5847 
and 0.6180, respectively. Find the chord of 31°. 


5= 0.0337 

c = -0.0003 
d= 0.0002 


(l Cl\ (1% &3 

0.5176 0.5513 0.5847 0.6180 

0.0337 0.0334 0.0333 

-0.0003 -0.0001 

0.0002 

n = (31 —30) -5- (32 — 30) =0.5 


a x = 0.5176 + 0.5(0.0337)4 
= 0.5345. 


0.5(-0.5)(-0.0003) . _ _ ( — 0.5)( — 1.5)(0.0002) 
- ~ -h 0.5-»- 


Logarithms (log). The hyperbolic or Napierian log of any number 
equals the common log X 2.3025851. The common log of any number 
equals the hyperbolic log (log,?) X0.4342945. 

Every log consists of a whole part (the characteristic) and a decimal part 
(the mantissa). The mantissa or decimal part only is given in the tables. 

The characteristic of the log of a number is one less than the number of 
figures to the left of the decimal point in the number. 

Log 3 = .47712, log 30 = 1.47712, log 300 = 2.47712, etc 

Log 0.3= — 1.47712, log 0.03= -2.47712, log 0.003= -3.47712, etc. 

Any logarithm with a negative characteristic as — 1.47712, may be written 
as 9.47712 — 10. (The sum of 9 and — 10 being — 1.) 

Formulas for Using Logarithms, log ab = log a + log b. 


log 


Toga — log b, loga & = 6 1oga. 


logy a = —^—, 













TABLE OP CHORDS. 


5 


Examples. 

5X4 (using logs); Log 5 = .69S97 
Log 4 = .60206 

Sum =1.30103, which is the log of 20, or the result re- 

quired. 

Multiply 0.5 by 0.04. 

log 0.5 =-1.69897= 9.69897-10 
log 0.04 = -2.60206 = 8.60206 - 10 

Their sum = 18.30103 - 20 = - 2.30103, or the log of 0.02. 
For 0.5-^0.04, diff. of logs= 1.09691- 0 = log of 12.5. 

Find nth root of 0.09. 

log 0.09 = - 2.95424 = 8.95424 -10 

divided by n (say 2) =4.47712 — 5= —1.47712, or log of 0.3. 

Raise 0.3 to nth power. 

log 0.3=-1.47712 = 9.47712-10 
multiplying by n (say 2) = 18.95424 — 20-2.95424 —log 0.09. 

Log jc= .49715, log—=—1.50285, log 7t 2 = .9943, 

7C 

log V7= .248575. x = 3.1415926536 +. 


TABLE OF CHORDS. 


Deg. 

Chd. 

Deg. 

Chd. 

Deg. 

Chd. 

Deg. 

Chd. 

Deg. 

Chd. 

2 

0349 

20 

.3473 

38 

.6511 

56 

.9389 

74 

1.2036 

4 

0698 

22 

.3816 

40 

.6840 

58 

.9700 

76 

1.2313 

n 

" 1047 

24 

.4158 

42 

.7167 

60 

1.0000 

78 

1.2586 

« 

1395 

26 

.4499 

44 

.7492 

62 

1.0301 

80 

1.2856 

10 

1743 

28 

.4838 

46 

.7815 

64 

1.0598 

82 

1.3121 

12 

2090 

30 

.5176 

48 

.8135 

66 

1.0893 

84 

1.3383 

14 

2437 

32 

.5513 

50 

.8452 

68 

1.1184 

86 

1.3640 

16 

2783 

34 

.5847 

52 

.8767 

70 

1.1471 

88 

1.3893 

18 

!3129 

36 

.6180 

54 

.9080 

72 

1.1756 

90 

1.4142 


3TENSURATION. 

AREAS OF PLANE FIGURES (A). 

Triangles. Take as base any side which will be intersected by a per¬ 
pendicular let fall from vertex of opposite angle. Len gth of base - b, l ength 

of side to the left = a, side to right = e. Then A^-^ya ^ 2b ) 

6/l Tr 2 apez e oTd! = If^ gt 5 amF^Sengths of parallel sides and perpendicular, 

r T?rcir' y, (r A -” adiuS diameter) = 4. Circumf. - ,i. 

Sector Of Circle. A =0.5rX length of arc = 0.008727r2X degrees marc. 
Segment of Circle. A =0.5[br — c(r—h)]. b = arc, c = base, h = height 

at Ellipse/ b Eq e uation referred to axes through center: a 2 j/ : *+W' = a*b* 
where a = semi-minor axis, b = semi-major axis and x and y are the abscissa 
Ind ordinate of any point on the perimeter. A = nab. Length of perimeter 

<a-5\ 2 . 1 


■n(a-{-b ) 




+ 


J_ ( a ~~ r \ ‘ 

\ n - 4 - h f 


+ 




4 \a-\-b) ' 64Va + 5 / ' 256\a + 6>' _ 

Para bola. Equation, origin at vertex = 2px, where.2 V is the parame- 


I tird UUia# 

ter, or double ordinate through focus 

2 xy 


Area of any portion from vertex 1 











































6 


MATHEMATICS 


Hyperbola. Equation: a 2 y 2 — b 2 x 2 = —a 2 b 2 . 

Cycloid. Length of curve = 4 times diam. of generating circle. 

Area =3 “ area “ 

Area of Amy Irregular Figure. Simpson’s Rule. Divide the length 

of the figure into an even number of equal parts and erect ordinates through 

the points of division to touch the boundary lines. Then A = 

where o = sum of first jmd last ordinates, fc = sum of even ordinates, c = sum 
of odd ordinates (excepting first and last) and d = common distance between 
ordinates. The greater the number of divisions the greater wall be the 
accuracy. 

LOGARITHMS OF NUMBERS. 


No. 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 


0 

00000 

04139 

07918 

11394 

14613 

17609 

20412 

23045 

25527 

27875 

30103 

32222 

34242 

36173 

38021 

39794 

41497 

43136 

44716 

46240 

47712 

49136 

50515 

51851 

53148 

54407 

55630 

56820 

57978 

59106 

60206 

61278 

62325 

63347 

64345 

65321 

66276 

67210 

68124 

69020 

69897 

70757 

71600 

72428 

73239 


00432 

04532 

08279 

11727 

14922 

17898 

20683 

23300 

25768 

28103 

30320 

32428 

34439 

36361 

38202 

39967 

41664 

43297 

44871 

46389 

47857 

49276 

50651 

51983 

53275 

54531 

55751 

56937 

58093 

59218 

60314 

61384 

62428 

63448 

64444 

65418 

66370 

67332 

68215 

69108 

69984 


00860 

04922 

08636 

12057 

15229 

18184 

20952 

23553 

26007 

28330 

30535 

32634 

34635 

36549 

38382 

40140 

41830 

43457 

45025 

46538 

48001 

49415 

50786 

52114 

53403 

54654 

55871 

57054 

58206 

59329 

60423 

61490 

62531 

63548 

64542 

65514 

66464 

67394 

68305 

69197 

70070 


70842 70927 
71684 71767 
72509 72591 
73320 73400 


01284 

05308 

08991 

12385 

15534 

18469 

21219 

23805 

26245 

28556 

30750 

32838 

34830 

36736 

38561 

40312 

41996 

43616 

45179 

46687 

48144 

49554 

50920 

52244 

53529 

54777 

55991 

57171 

58320 

59439 

60531 

61595 

62634 

63649 

64640 

65610 

66558 

67486 

68395 

69285 

70157 

71012 

71850 

72673 

73480 


01703 

05690 

09342 

12710 

15836 

18752 

21484 

24055 

26482 

28780 

30963 

33041 

35025 

36922 

38739 

40483 

42160 

43775 

45332 

46835 

48287 

49693 

51055 

52375 

53656 

54900 

56110 

57287 

58433 

59550 

60638 

61700 

62737 

63749 

64738 

65706 

66652 

67578 

68485 

69373 

70243 

71096 

71933 

72754 

73560 


02119 

06070 

09691 

13033 

16137 

19033 

21748 

24304 

26717 

29003 

31175 

33244 

35218 

37107 

38917 

40654 

42325 

43933 

45484 

46982 

48430 

49831 

51189 

52504 

53782 

55023 

56229 

57403 

58546 

59660 

60746 


6 


02531 

06446 

10037 

13354 

16435 

19312 

22011 

24551 

26951 

29226 

31387 


19590 
22 
24797 
27184 
29447 
31597 


33445 33646 
35411 35603 
37291:37475 
39094 39270 
40824 40993 
42488142651 
44091(44248 
45637 45788 
47129 47276 
48572 48714 

49969 50106 
51322 51455 
5263452763 
5390854033 
55145 55267 
56348 56467 
57519,57634 
58659 58771 
59770 59879 
60853 60959 


61805 61909 
62839 62941 
63849 63949 


64836 

65801 

66745 

67669 

68574 

69461 

70329 

71181 

72016 

72835 

73640 


64933 

65896 

66839 

67761 

68664 

69548 

70415 


62014 
63043 
64048 
65031 
65992 
66932 
67852 
168753 
69636 
70501 


71265 71349 
72099 72181 
72916 72997 
73719 73799 


8 

9 

Diff. 

03342 

03743 

415 

107188 

07555 

379 

10721 

11059 

344 

13988 

14301 

323 

17026 

17319 

298 

19866 

20140 

281 

22531 

22789 

264 

25042 

25285 

249 

27416 

27646 

234 

29667 

29885 

222 

31806 

32015 

212 

33846 

34044 

202 

35793 

35984 

193 

37658 

37840 

185 

39445 

39620 

177 

41162 

41330 

170 

42813 

42975 

164 

44404 

44560 

158 

45939 

46090 

153 

47422 

47567 

148 

48855 

48996 

143 

50243 

50379 

138 

51587 

51720 

134 

52892 

53020 

130 

54158 

54283 

126 

55388 

55509 

122 

56585 

56703 

119 

57749 

57864 

116 

58883 

58995 

113 

59988 

60097 

110 

61066 

61172 

107 

62118 

62221 

104 

63144 

63246 

102 

64147 

64246 

99 

65128 

65225 

98 

66087 

66181 

96 

67025 

67117 

95 

67943 

68034 

92 

68842 

68931 

90 

69723 

69810 

88 

70586 

70672 

86 

71433 

71517 

84 

72263172346 

82 

73078 

73159 

81 

73878 

73957 

80 















































61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 

99 

Not 

cura 

! fou 

Sph 

Rin 


7 

Diff. 

78 

77 

75 

74 

73 

72 

71 

70 

69 

68 

67 

66 

64 

63 

63 

62 

61 

60 

59 

58 

57 

57 

56 

55 

54 

54 

53 

53 

52 

51 

51 

50 

49 

49 

48 

48 

48 

47 

47 

46 

46 

45 

45 

44 

44 

For 

>uld 

D = 


' LOGARITHMS of numbers. 
LOGARITHMS OF NUMBERS {Continued). 


0 


74036 74115174194174273 
74819 74896174974:75051 
75587 75664 75740 75815 
76343 76418 76492 76567 
77085 77159 77232 77305 
77815 77887 77960178032 


78533 

79239 

79934 

80618 

81291 

81954 

82607 

83251 

83885 

84510 

85126 
85733 
86332 
86923 
875 06 
88081 
886 49 
89209 


78604 

79309 

80003 

80686 

81358 

82020 

82672 

83315 

83948 

84572 

85187 

85794 

86392 

86982 

87564 

88138 

88705 

89265 


89763189818 
>0309 90363 


78675 

79379 

80072 

80754 

81425 

82086 

82737 

83378 

84011 

84634 


78746 

79449 

80140 

80821 

81491 

82151 

82802 

83442 

84073 

84696 


85248 85309 
85854 85914 
86451 86510 
87040:87099 
87622 87680 


88196 

88762 


88252 

8S818 


90849 

91381 

91908 

92428 

92942 

93450 

93952 

94448 

94939 

95424 

95904 

96379 

96848 

97313 

97772 

98227 

98677 

99123 

99564 


90902 

91434 

91960 

92480 

,92993 

93500 

94002 

94498 

94988 

95472 

95952 

96426 

96895 

97359 

97818 

98272 

98722 

99167 

99607 


89321189376 
89873 89927 
90417 90472 


90956 

91487 

92012 

92531 

93044 

93551 

94052 

94547 

95036 

95521 


95999 

96473 

96942 

97405 

97864 

98318 

98767 

99211 

99651 


91009 

91540 

92065 

92583 

93095 

93601 

94101 

94596 

95085 

95569 


74351 

75128 

75891 

76641 

77379 

78104 

78817 

79518 

80209 

80889 

81558 

82217 

82866 

83506 

84136 

84757 

85370 

85974 

86570 

87157 

87737 

88309 

88874 

89432 

89982 

90526 


5 

74429 

75205 

75967 

76716 

77452 

78176 

78888 

79588 

80277 

80956 

81624 

82282 

82930 

83569 

84198 

84819 

85431 

86034 

86629 

87216 

87795 

88366 

88930 

89487 

90037 

90580 


91062 91116 


96047 

96520 

96988 

97451 

97909 

98363 

98811 

99255 

99695 


91593 

92117 

92634 

93146 

93651 

94151 

94645 

95134 

95617 

96095 

96567 

97035 

97497 

97955 

98408 

98856 

99300 

99739 


91645 

92169 

92686 

93197 

93702 

94201 

94694 

95182 

95665 

96142 

96614 

97081 

97543 

98000 

98453 

98900 

99344 

99782 


6 

74507 

75282 

76042 

76790 

77525 

78247 

78958 

79657 

80346 

81023 

81690 

82347 

82995 

83632 

84261 

84880 

85491 

86094 

86688 

87274| 

87852 

88423 

88986 

89542 

90091 

90634 


74586 

75358 

76118 

76864 

77597 

78319 

79029 

79727 

80414 

81090 

81757 

82413 

83059 

83696 

84323 

84942 


91169 

91698 

92221 

92737 

93247 

93752 

94250 

94743 

95231 

95713 

96190 

956611 

97128 

97589 

98046 

98498 

98945 

99388 

99826 


85552 

86153 

86747 

87332 

87910 

88480 

89042 

89597 

90146 

90687 


74663 

75435 

76193 

76938 

77670 

78390 

( 

< 

1 
l 

£ 


91222 

91751 

92273 

92788 

93298 

93802 

94300 

94792 

95279 

95761 

^96237 

96708 

97174 

97635 

98091 

98543 

98989 

99432 

99870] 


i 
£ 

£ 

£ 

£ 

£ 

£ 

£ 

S 
fl 

91275 

91803 

92324 

92840 

93349 

93852 

94349 

94841 

95328 

95809 


96284 

96755 

97220 

97681 

98137 

98588 

99034 

99476 

99913 


91328 

91855 

92376 

92891 

93399 

93902 

94399 

94890 

95376 

95856 


I 


96332 

96802 

97267 

97727 

98182 

98632 

99078 

99520 

99957 


—The differences in the last column are mean v£ 
values the difference between any two consecuth 
I by subtraction. 


URFACES (A) AND VOLUMES (V) OF 

•e. A = 4*r2 = «R V = ~ = 0.5236<H. 

o 

of Circular Cross-section. A=9.8696jDd. F = 
liameter — d\ d = diam. of cross-section.) 





















































































MATHEMATICS. 


Segment ot Sphere. A -2»*-are» ot ba»+*W (fc-heightX 

F-*A’(r--§). 

Cone. A=W^Th 2 '. V = 0.2618d 2 h (h = vert. height). 

Conic Frustum. A =-^r(D + d)Xslant height, h. 

V=y 2 (D 2 + Dd + d 2 ). 

Cylinder. F = 0.7854 d 2 h. (d is the revolving axis of cyh and ellipsoid.) 
Ellipsoid. F = 0.5236 Dd 2 . Paraboloid. F-1.5708 r h. 

Pyramid. F 3 *^ Xarea of base. 

Frustum ot Pyramid. V-|(A+a + ^) (Aanda-areasof bases). 

TRIGONOMETRY. 



Formulas. (A, B and C are angles.) 
sin A . . cos A 


n A= ^A’ " Ub ~~sin A - cos A’ sm/i 

2 \ cos 2 A = 1 ; versin A = 1 — cos A ; covers A 1 sm A. 
(A±B) =sin A cos £±cos A sin B. 

(A ± B) — cos A cos BT sm A sin d. 

‘ * „ A . o A 

cos 2 ~~ sin- 4 -g-. 

A A 

cos A = 2 sin 2 y* 1 + cos A =2 cos 2 -j. 

. A=2tan|--[l-tan 2 4]- sin A + cos A = sin (-| + a)v^7 
/ n \ - 1 — cos A 4 

A-sin A=sin^-AJ V2. cos a 


cot A 


secA “^rA ;cosec ^”ri^ : tanj 4 “JSTA- 


A A 
A = 2 sin cos -g. cos A 


a. ~— — — \ 4 / cos 71 

(A ± .B) = [tan A ±tan B]-KlTtan A tan _B] 
(A ±B) =[cot A cot i?Tl] + [cot A±cot B]. 

„ „ . A±5 AT B 

A ±sin B = 2 sin —x — cos — ■= — . 

a Ib a ±b 

! A + COS B = 2 cos —^— COS 


= tan A tan 


. ATB . 

■ 2 sin —g— sln 

■B) 


2 * 

A — B 


A — cos £ = 

A sin B = i cos (A—B)—b cos (A +5). 

; A cos B = i cos (A + B) + i cos ( A — B). 

A cos JS = ^ sin (ATB)Tb sin (A — B). 

3A = 3 sin A — 4 sin 3 A. cos 3A = 4 cos 3 A — 3 cos A. 

,s gi n A)« = cos nA±i sin nA (i = v^l). 





















NATURAL TRIGONOMETRICAL FUNCTIONS 


9 


If A + B + C = 180° = 7r (the three angles of a triangle), then 

ABC 

sin A + sin B + sin C = 4 cos — cos — cos —. 

£ £ JL 

A B C 

cos A + cos B + cos C = 1 + 4 sin — sin — sin —. 

J J J 

tan A + tan B + tan C = tan A tan B tan C. 


NATURAL TRIGONOMETRICAL FUNCTIONS. 


Degs. 

Sine. 

Tangent. 


Degs. 

Sine. 

Tangent. 


0 

.00000 

.00000 

90 

46 

.71934 

1.03553 

44 

1 

.01745 

.01746 

89 

47 

.73135 

1 07237 

43 

2 

.03490 

.03492 

88 

48 

.74314 

1.11061 

42 

3 

.05234 

.05241 

87 

49 

.75471 

1.15037 

41 

4 

.06976 

.06993 

86 

50 

.76604 

1.19175 

40 

5 

.08716 

.08749 

85 

51 

.77715 

1.23490 

39 

6 

.10453 

.10510 

84 

52 

.78801 

1.27994 

38 

7 

.12187 

.12278 

83 

53 

.79864 

1.32704 

37 

8 

.13917 

.14054 

82 

54 

.80902 

1.37638 

36 

9 

.15643 

.15838 

81 

55 

.81915 

1*42815 

35 

10 

.17365 

.17633 

80 

56 

.82904 

1.48250 

34 

11 

.19081 

.19438 

79 

57 

.83867 

1.53987 

33 

12 

.20791 

.21256 

78 

58 

.84805 

1.60033 

32 

13 

.22495 

.23087 

77 

59 

.85717 

1.66428 

31 

14 

.24192 

.24933 

76 

60 

.86603 

1.73205 

30 

15 

.25882 

.26795 

75 

61 

.87462 

1.80405 

29 

16 

.27564 

.28675 

74 

62 

.88295 

1.88073 

28 

17 

.29237 

.30573 

73 

63 

.89101 

1.96261 

27 

18 

.30902 

.32492 

72 

64 

.89879 

2.05030 

26 

19 

.32557 

.34433 

71 

65 

.90631 

2.14451 

25 

20 

.34202 

.36397 

70 

66 

.91355 

2.24604 

24 

21 

.35837 

.38386 

69 

67 

.92050 

2.35585 

23 

22 

.37461 

.40403 

68 

68 

.92718 

2.47509 

22 

23 

.39073 

.42447 

67 

69 

.93358 

2.60509 

21 

24 

.40674 

.44523 

66 

70 

.93969 

2.74748 

20 

25 

.42262 

46631 

65 

71 

.94552 

2.90421 

19 

26 

.43837 

.48773 

64 

72 

.95106 

3.07768 

18 

27 

.45399 

.50952 

63 

73 

.95630 

3.27085 

17 

28 

.46947 

.53171 

62 

74 

.96126 

3.48741 

16 

29 

.48481 

.55431 

61 

75 

.96593 

3.73205 

15 

30 

.50000 

.57735 

63 

76 

.97030 

4.01078 

14 

31 

.51504 

.60086 

59 

77 

.97437 

4.33148 

13 

32 

.52992 

.62487 

58 

78 

.97815 

4.70468 

12 

33 

.54464 

.64941 

57 

79 

.98163 

5.14455 

11 

34 

.55919 

.67451 

56 

80 

.98481 

5.67128 

10 

35 

.57358 

.70021 

55 

81 

.98769 

6.31375 

9 

36 

.58779 

.72654 

54 

82 

.99027 

7.11537 

8 

37 

.60182 

.75355 

53 

83 

.99255 

8.14435 

7 

38 

.61566 

.78129 

52 

84 

.99452 

9.51436 

6 

39 

.62932 

.80978 

51 

85 

.99619 

11.43005 

5 

40 

.64279 

.83910 

50 

86 

.99756 

14.30067 

4 

41 

.65606 

.86929 

49 

87 

.99863 

19.08114 

3 

42 

.66913 

.90040 

48 

88 

.99939 

28.63625 

2 

43 

.68200 

.93252 

47 

89 

.99985 

57.28996 

1 

44 

.69466 

.96569 

46 

90 

1.00000 

Infinite 

0 

45 

.70711 

1.00000 

45 






Cosine. 

Cotangent. 

Degs. 


Cosine. 

1 

Cotangent. 

Degs. 


For intermediate values reduce angles from degrees, minutes ana seconds 
to degrees and decimal part of a degree (e.g., 46° 21' 30" = 46.3u83 ) and 
employ interpolation formula. 





































CHEMICAL DATA 


Atomic Weights and Symbols of Elements. 


Aluminum. A1 

Antimony.kb 

Argon. A 

Arsenic. As 

Barium.Ba 

Bismuth. Bi 

Boron. B 

Bromine. Br 

Cadmium. Cd 

Ciesium.Cs 

Calcium. Ca 

Carbon. C 

Cerium. Ce 

Chlorine.. . • • Cl 

Chromium. Cr 

Cobalt.• Co 

Columbium (Nio¬ 
bium). Cb 

Copper. Cu 

Erbium. 

Fluorine. F 

Gadolinium. Gd 

Gallium.. Ga 

Germanium. Ge 

G 1 u c i n u m (Beryl- G1 

burn).. • . 

Gold. Au 

Helium. He 

Hydrogen.H 

Indium. In 

Iodine.I 

Iridium.Ir 

Iron. Fe 

Krypton.. K 

Lanthanum. La 

Lead. Pb 

Lithium. Li 

Magnesium.Mg 

Manganese. Mn 

Mercury. Hg 


26. 

9 

119. 

3 

39. 

6 

74. 

4 

136. 

4 

206. 

9 

10. 

9 

79. 

36 

111. 

6 

132 


39. 

,8 

11. 

91 

139 


35, 

.18 

51. 

.7 

58. 

.56 

93 

.3 

63, 

.1 

164, 

.8 

18, 

.9 


155 

69.5 
71.9 

9.03 

195.7 

4 

1.00 

113.1 

125.9 

191.5 

55.5 
81.2 

137.9 
205.35 

6.98 

24.18 

54.6 

198.5 


Molybdenum. 

. Mo 

95.3 

Neodymium. 

. Ne 

142.5 

Neon. 


19.9 

Nickel. 

. Ni 

58.3 

Nitrogen. 

. N 

13.93 

Osmium. 

. Os 

189.6 

Oxygen. 

. O 

15.88 

Palladium. 

. Pd 

106.7 

Phosphorus. 

. P 

30.77 

Platinum. 

. Pt 

193.3 

Potassium. 

. K 

’38.86 

Praseodymium. 

. Pr 

139.4 

Radium. 

. Ra 

223.3 

Rhodium. 

. Rh 

102.2 

Rubidium. 

. Rb 

84.8 

Ruthenium. 

. Ru 

100.9 

Samarium. 

. Sm 

148.9 

Scandium. 

. Sc 

43.8 

Selenium. 

. Se 

78.6 

Silicon. 

. Si 

28.2 

Silver. 

• Ag 

107.12 

Sodium. 

. Na 

22.88 

Strontium. 

. Sr 

86.94 

Sulphur. 

. S 

31.83 

Tantalum. 

. Ta 

181.6 

Tellurium. 

. Te 

126.6 

Terbium. 

. Tb 

158.8 

Thalium. 

. T1 

202.6 

Thorium. 

. Th 

230.8 

Thulium. 

. Tm 

169.7 

Tin... 

. Sn 

118. 1 

Titanium; .. 

. Ti 

47.7 

Tungsten. 

. W 

182.6 

Uranium. 

. U 

236.7 

Vanadium. 

. V 

50.8 

Xenon. 

. X 

127 

Ytterbium. 

. Yb 

171.7 

Yttrium. 

. Yt 

88.3 

Zinc. 

. Zn 

64.9 

Zirconium. 

. Zr 

89.9 


Calculation of the Percentage Composition of Substances. 

(1) Add together the atomic weights of the elements to obtain the molec¬ 
ular weight of the compound. (2) Multiply the atomic weight of the 
element to be calculated by the number of atoms present (as indicated by 
the subscript number) and by 100, and divide by the molecular weight of 
the compound. 

Example. Find the percentage of sulphur in sulphuric acid (H 2 SO 4 ). 
H 2 + S + 0 4 

(1 X2)+31.83 + (15.88X4) =97.35, or the molecular weight. 3183 ■+• 97.35 
= 32.59, or the percentage of sulphur in the acid. 

Weights of Gases. Avogadro’s law: “In equal volumes of all gases 
there are the same number of molecules.” It follows from this law that 
the weights of equal volumes of all gases are proportional to their molec¬ 
ular weights. 

The molecular or formula weight in grams of any gas occupies 22.4 liters 
at 0° C. and 760 mm. pressure. 

Example. Find the weight of one liter of carbon dioxide (C0 2 ). Molec¬ 
ular wt. of C0 2 = 11.91 + (15.88X2) =43.67. 43.67 grams = 22.4 liters, 

or 1 liter weighs 1.95 grams. 

(1 cu. ft. = 28.317 liters; 1 liter = 0.03532 cu. ft.; 1 lb. = 453.5924 grams; 
1 gram =0.0022046 lb.) 


10 























































































MATERIALS 


Cast Iron (C. I.). Sp. gr. = 7.21; wt. per cu. in. =0.261 lb. Fusing 
point of white iron = 1,962° F.;—gray iron, 2,192° F. Chemically com¬ 
posed of iron (Fe), carbon (C) (graphitic and combined), silicon (Si), phos¬ 
phorus (P), sulphur (S) and manganese (Mn). Contains 3.5 to 4% of 
total carbon, the hardness of castings varying directly with the amount of 
combined carbon. Si (from 0.5 to 3.5%) produces softness and strength 
proportional to amount contained. (Best at 1.8%.) S beyond 0.15% is 
prejudicial, producing blow-holes and brittleness when hot. P promotes 
fluidity but causes brittleness when in excess of 1%. Mn assists the car¬ 
bon in combining and confers the property of chilling. It should not ex¬ 
ceed 1%. 

Wrought Iron (W.'I.). Sp.gr. = 7.78; wt. per cu. in. =0.282 lb. Con¬ 
sists of over 99% pure iron+ 0.3% combined carbon+ 0.14% each of S, 
Si and P. 

Steel. Cast steel, sp. gr. = 7.92; wt. per cu. in. = 0.286 lb. Forged steel, 
sp. gr.= 7 82; wt. per cu. in. = 0.283 lb. Fusing point =2 500 to 2,700° F. 

Temper (or content of carbon). Castings, 0.3 to 0.4%; forgings, 0.25 
to 0.3%: chain®. 0.15 to 0.18%; laminated springs. 0.4 to 0 6%; boiler 
plates, 0.17 to 0.2%; same, for welding, 0.15 to 0.17%; tool steel, up to 
1.35%. 

Manganese Steel (containing 14% Mn) has double the strength of ordi¬ 
nary steel combined with great hardness. 

Nickel Steel (3 to 5% Ni) has 30% greater tenacity and 75% greater 
elastic strength than ordinarv mild steel, along with equal ductility. Har- 
vevized, for ship armor, it offers the same resistance with 43% less weight. 

Chrome Steel (0.4% C+1% of Chromium (Cr) + 2% Ni) is of extreme 
hardness (self-hardening) and is used for safe walls, projectiles, and cutting 

Tungsten Steel (Mushet’s) is a self-hardening steel for tools, shells, etc. 
(1.70% 0+0.42% Si+0.25% Mn +8.5% Tungsten i Vv ) >. _ 

Copper (Cu). Sp.gr. = 8 878 (wire and rolled); wt. per cu. ih. = 0.321 lb.; 
fusing point = 1,950° F. Zinc (Zn). Sp. gr. = 6.86 (cast); wt. per cu. in. = 
0 248 lb.; fusing point = 787° F. Tin (Sn). Sp.gr. = 7 3; wt- per cu. in.= 
0.264 lb; fusing point = 446°F. Aluminum (Al). Sp.gr =2 56 (cast) 
and 2.68 (rolled); wt. per cu. in. =0.092 lb. (cast) and 0.097 lb. (rolled). 
Fuses at 1 213° F. 

Mercurv (Hg). Sp. gr =13.619 (at 32° F ) and 13.58 (at 60° F.); wt. 
per cu in. = 0 493 lb (at 32° F ) and 0.491 lb. (at 60°F.). Fuses at —39° F. 

Gun Metal Bronze (80 to 90% Cu + 20to 10% Sn) Strong and tough 
Increasing the content of tin increases the hardness Phosphor Bronze 
(85% Cu + 15% Sn + 0 5 to 0.75% P) has the toughness of W I. Man¬ 
ganese Bronze (81% Cu + 12% Sn + 7% Mn) is even stronger. Silicon 
Bronze (Cu + 3 to 5% Si) has a breaking stress of 55,000 to 75,000 lb. per 
so. in., but at and around 5% Si, is brittle. Aluminum Bronze (Cu + 5 
to 11% Al) has a slightly greater strength. Brass (60 to 70% Cu + 40 to 
30% Zn). Babbitt (89.3% Sn + 3.6% Cu + 7.1% Sb (antimony)). 


Alloys. (E. A. Lewis, Engineering, 3-31-05.) 


Cu. 

For steam or gas pressure.... 87 
“ hydraulic pressure...... 86 

• ‘ bearings. 84 

Phosphor-bronze, . .. 

Copper castings.yy. to 


Sn. 

9 

12 

8 

14 


Zn. 

2 

2 


Pb, 

2 

8 

2 


P. 


0.05 


Si. 


0.25 


11 







12 


MATERIALS 


Delta Metal (92.4% Cu + 2.38% Sn + 5.2% Pb (lead)). 

Magnolia Metal (83-55% Pb + 16.45% Sn). Tobin Bronze (59%, Cu + 
2.16% Sn +0.3% Pb +38.4% Zn). Solder. 2 Sn + 1 Pb fuses at 340 F., 
1 on+ 2 Pb fuses at 441° F., and 20 Sn + 1 Pb (for aluminum) at 550 -b • 


Woods. Average Sp. Gr. and Weights per Cu. Ft. 


Sp. Gr. Wt. 


Ash. 

.. 0.72 

45 

Beech. . .. 

. . .73 

46 

Birch. . . . 

. . .65 

41 

Cedar. . . . 

. .. .62 

39 

Elm. 

. .. .61 

38 


Sp. Gr. Wt. 


Fir. 

0.59 

37 

Hickory. . .. 

.77 

48 

Hemlock. . . 

.38 

24 

Maple. 

.68 

42 

White Oak.. 

.77 

48 


Sp. Gr. Wt. 


Red Oak. . . 

0.74 

46 

White Pine. 

.45 

28 

Yellow Pine. 

.61 

38 

Poplar. 

.48 

30 

Spruce. 

.45 

28 


Stones and Miscellaneous Building Materials. 


Asbestos. 

Asphaltum. 

Brick (com.). 

“ (pressed). 

“ (fire). 

Clay. 

Cement, Rosendale. . 

Portland.. . . 

Earth (loose). 

Granite,. 


Sp. Gr. 

Wt. 


Sp. Gr. 

Wt. 

3.07 

192 

Graphite. . . . 

. 2.16 

135 

1.39 

87 

Glass. 

. 2.64-2.93 

164-183 

1 6 

100 

Limestone. . . 

. 2.7-3.2 

170-200 

2.16 

135 

Marble. 

. 2.56-2.88 

160-180 

2.24 

140 

Mica. 

. 2.8 

173 

1.92 

120 

Quartz. 

.2.64 

165 

0.96 

60 

Rubber. 

. 0.933 

58.4 

1.25 

78 

Sand. 

. 1.9 

122 

1.28 

80 

Sandstone. . 

. 2.4 

150 

2.6 

165 

Slate. 

. 2.88 

180 


(Wts. in lbs. per cu. ft.) 


Weight of Rods, Bars, Plates, Tubes, and Spheres of Metals. 



Lbs. 

Square 

Flat 

Round 

Plates, 



Bars, 

Bars, 

Rods, 


Spheres, 

Material. 

per 

lbs. per 

lbs. per 

lbs.per 

lbs. per 

lbs. 


tv* 

lin. ft. 

lin. ft. 

lin. ft. 

sq. ft. 


Cast Iron. 

450 

3.125s 2 


2.454d 2 

37. 5t 

0.1363d 3 

Wrought Iron. . 

480 

3.333s 2 

<V) ^ ° 

2.618 d 2 

40 t 

0.1455d 3 

Steel. 

489.6 

3.4s 2 

13 G v r 

2.670d 2 

40.8 1 

0.1484d 3 

Copper. 

552 

3.833s 2 

^ G rt 

3.010d 2 

46i t 

0.1673d 3 

Brass (65 Cu + 



j§ url g 




35 Zn). 

523.2 

3.633s 2 


2.853d 2 

43. 6t 

0.1586d 3 

Aluminum. 

166.5 

1.156s 2 

m 

0.908d 2 

13.875 t 

0.0504d 3 


For tubes, multiply numerical coeff. for round rods by (d 2 — dr). 

For hollow spheres, multiply numerical coeff. for spheres by (d 3 —di 3 ). 
s = side of square, 6 = breadth, < = thickness, d = external diam., di = inter 
nal diam., all in inches. 


Weight of Square and Round Wrought Iron Bars in Tbs. per 

Lineal Foot. 


s or 
d. 

Rd. 

Sq. 

s or 
d. 

Rd. 

Sq. 

s or 
d. 

Rd. 

Sq. 

iV 

.010 

.013 

tt 

1.237 

1.576 

H 

6 

913 

8 

802 

| 

.041 

.052 

i 

1.473 

1.875 

11 

8 

018 

10 

21 

TS 

.092 

.117 

1 3 

1 6 

1.728 

2.201 

11 

9 

204 

11 

72 

i 

.164 

.208 

l 

2.004 

2.552 

2 

10 

47 

13 

33 

ve 

.256 

.326 

IA 

16 

2.301 

2.930 

21 

13 

25 

16 

88 

i 

.368 

.469 

1 

2.618 

3.333 

21 

16 

36 

20 

83 

'lS 

.501 

.638 

1* 

3.313 

4.219 

21 

19 

8 

25 

21 

i 

.654 

.833 

H 

4.091 

5.208 

3 

23 

56 

30 


TS 

.828 

1.055 

11 

4.95 

6.302 

31 

32 

07 

40 

83 

i 

1.023 

1.302 

H 

5.89 

7.5 

4 

41 

89 

53 

33 



(s = side of 

sq. in in. 

d = diam 

in in 

.) 










































MISCELLANEOUS TABLES AND DATA. 


13 


Weight of Flat W. I. Bars (1 in. wide) in Lbs. per Lineal Foot. 


Thick¬ 

ness. 

Lbs. 

Thick¬ 

ness. 

Lbs. 

Thick¬ 

ness. 

Lbs. 

iV 

.208 

TS 

1.46 

i 

2.50 

jr 

.417 

* 

1.67 

I 3 

1 6 

2.71 

TS 

.625 

9 

J 6 

1.88 

l 

2.92 

i 

.833 

i 

2.08 

1 5 

1 6 

3.13 

A 

1.04 

T6 

2.29 

1 

3.33 

t 

1.25 

Thickness in in. 

For steel add 2% 


Weight of Iron, Steel, Copper and Brass Sheets per Square Foot. 

Lbs. per sq. ft. = thickness in inches (obtained from gauge tables) X40, 
40.8, 46, or 43.6 respectively. 


Corrugated and Flat Iron. Lbs. per Sq. Ft. 


Thickness 

Flat, 

Corr., 

Thickness 

Flat, 

Corr., 

in in. 

lbs. 

lbs. 

in in. 

lbs. 

lbs. 

.065 

2.61 

3.28 

.028 

1.12 

1.41 

.049 

1.97 

2.48 

.022 

0.88 

1.11 

.035 

1.4 

1.76 

.018 

0.72 

0.91 


If galvanized, add 0.34 lb. per sq. ft. for flat plates and 0.43 lb. for cor¬ 
rugated plates. End laps 4 in. and 6 in. Side laps = l corrugation = 2.5 in. 

Tin Plates. (Tinned sheet steel.) Usual roofing sizes are 14X20 and 
20X28 (in inches). No. 29 B. W. G. weighs 49.6 lb. per 100 sq. ft.; No. 27 
weighs 62 lbs. per 100 sq. ft. 

Roofing Slate. (1 cu. ft. weighs 175 lb.) 


Thickness in in. i A i i h I i 

Lbs. per sq.ft. 1.81 2.71 3.62 5.43 7.25 9.06 10.88 


Slates are generally laid so that the third slate overlaps the first by 
3 in. Sq. in. of roof covered by 1 slate =0.56(Z —3). No. of slates required 
for 1 square (100 sq. ft.) = 28,800-^-6(2 — 3). (b and l are breadth and 

length in in.) Sizes: 6 to 9X12, 7 to 10X14, 8 to 10X16, 9 to 12X8, 
10 to 16X20, 12 to 14X22, 12 to 16X24, 14 to 16X26. (Increases by 
steps of 1 in.) 

Pine Shingles. No. per 100 sq. ft. = 3,600-^-no. of inches exposed to 
weather. Wt. in lbs. of 100 sq. ft. = 864-r-no. of inches exposed to weather. 

Skylight and Floor Glass. Lbs. per sq. it. = 13 X thickness in inches. 

Flagging. Wt. in lbs. per sq. ft. = 14 X thickness in inches. 

Approximate Weights of Roofing Materials. (Lbs. per 100 sq. ft.) 
1 in. sheathing: spruce, 200; northern yellow pine, 300; southern yellow 
pine, 400; chestnut and maple, 400; ash and oak, 500. Shingles, 200; 
i in. slate, 900; tV in. sheet iron, 300; do., with lath, 500; corrugated iron, 
100-375; galvanized flat, 100-350; tin, 70-125; felt and asphalt, 100; 
felt and gravel, 800-1,000; skylights (glass Ts~i), 250-700; sheet lead, 
500-800; copper, 80-125; zinc, 100-200; flat tiles, 1,500-2,000; do., with 
mortar, 2,000-3,000; pan tiles, 1.000. 

W T eight of Cast-iron Pipe per Lineal Foot. Wt. inlbs. = 9.81hYi-l-0, 
where d and t are the internal diam. and thickness of metal in in. The wt. 
of the two flanges = wt. of 1 ft. of pipe. For copper, multiply by 1.226; 
for W. I., by 1.067. 

Weight of Cast-iron Water and Gas Pipes per Lineal Foot. 


Size in in. 4 

8 

12 

16 

20 

24 

30 

36 

42 

48 

60 

Water, lbs. per ft. 22 

42 

75 

125 

200 

250 

350 

475 

600 

775 

1330 

Gas, “ “ “ 17 

40 

70 

100 

150 

184 

250 

350 

383 

542 

900 


Thickness of Cast-iron W'ater Pipes. 

t = 0.00006(ft - 2 , ))d + 0.333— 0.0033d, 

where ft = head of water in feet, i ' d d are thickness and diam. in in. 

Riveted Hydraulic Pipe. (Telton Water Wheel Co.) Head in feet 
that pipe will safely stand = 48,600/! +-d. Weight in lbs. per lin. ft. = cdt. 
c=15 for 4 in. pipe 14 up to 8 in. pipe, 13 up to 12 in., 12.5 up to 24 in. 
and 12 up to 42 in. pipe. 





14 


MATERIALS 


Wrought-iron Pipe Dimensions and Threads. U. S. Standard 


Internal Diam 




io 

CO 

0) . 

5* 

m t- 

• 

• r " 4 

•—•4 

a a 

<D 

Cu . 

. fl 

< 

03 sh 

0) a) 

a 

3 .S 

« 

<5 

.2 a 
^■ h 

H 

i-i 

A 1-4 
H 

l 

.270 

.068 

.24 

27 

i 

.364 

.088 

.42 

18 

4 

i 

.494 

.091 

.56 

18 

o 

h 

. 623 

. 109 

.84 

14 

£ 

i 

.824 

.113 

1.12 

14 

4 

1 

1.048 

.134 

1.67 

11.5 

11 

1.38 

.140 

2.24 

11.5 

R 

1.611 

.145 

2.68 

11.5 

2” 

2.067 

.154 

3.61 

11.5 

21 

2.468 

.204 

5.74 

8 

3 

3.067 

.217 

7.54 

8 

31 

3.548 

.226 

9 . 

8 

4 

4.026 

.237 

10.66 

8 


Internal Diam. 


• 

.2.3 

■ai 

co 

CO 

0J . 

a a 

a . 

c3 m 

£ a 

o-- 

Z 

^ r* 

< 

.2 a 

r-> 

H 

Of 

A 

-a 

H 

44 

4.508 

.246 

12. 

49 

8 

5 

5.045 

.259 

14. 

50 

8 

6 

6.065 

.28 

18. 

76 

8 

7 

7.023 

.301 

23. 

.27 

8 

8 

7.982 

.322 

28. 

. 18 

8 

9 

9.001 

.344 

33 

.70 

8 

10 

10.019 

.366 

40 


8 

11 

11. 

.375 

45 


8 

12 

12. 

.375 

49 


8 

13 

13.25 

.375 

54 


8 

14 

14.25 

.375 

58 


8 

15 

15.25 

.375 

.62 


8 


Standard Boiler Tubes. Lap-welded Charcoal Iron. 

& Co.) 


Outside 
diam. in. 

1 

i 

i 

i 

2 

i 

i 

i 

3 

i 

Surface 


Inside 
diam. in. 

0.856 
1.106 
1.334 
1.56 
1.804 
2.054 
2.283 
2.533 
2.783 
3.012 

f tube 1 ft 


Lbs. 
per ft. 

0.708 

0.900 

1.25 

1.665 

1.981 

2.238 

2.755 

3.045 

3.333 

3.958 

long in sq. 


Outside Inside 
diam. in. diam. in. 


3* 

i 

4 

* 

5 

6 

7 

8 
9 

10 


3.262 

3.512 

3.741 

4.241 

4.72 

5.699 

6.657 

7.636 

8.615 

9.573 


ft. = 0.2618 Xdiam. in in 


(Morris Tasker 


Lbs. 
per ft. 
4.272 
4.59 
5.32 
6.01 
7.226 
9.346 
12.435 
15.109 
18.002 
22.19 


Wrought-iron Welded Tubes. Extra Strong. 


Nominal 
diam. in. 


1 

t 

# 

* 

1 

1 

i 

i 

2 

* 

3 

* 

4 


Actual Diameters 


Outside. 

0.405 

0.54 

0.675 

0.84 

1.05 

1.315 

1.66 

1.9 

2.375 

2.875 

3.5 
4. 

4.5 


Inside, Ex 
Strong. 

0.205 

0.294 

0.421 

0.542 

0.736 

.051 

1.272 

1.494 

1.933 

2.315 

2.892 

3.358 

3.818 


in in. 

--- — 

Inside, Double 
Ex. Strong. 


0.244 

0.422 

0.587 

0.884 

1.088 

1.491 

1.755 

2.284 

2.716 

3.136 


prox 


Lead Pipe. Safe working pressure in lbs per sq. ia.*= 1-000/ : d. Ap- 
x wt in lbs. per ft-= 15 5<(caliber + 0- t (thickness) and d (diam.) in in. 








MISCELLANEOUS TABLES AND DATA. 15 


Number of Square and Hexagonal Nuts in 100 lbs. (U. S. 

Standard; chamfered, trimmed and punched for standard taps.) 


Bolt 
diam. 
in in. 

No. 

Sq. 

No. 

Hex. 

Bolt 
diam. 
in in. 

No. 

Sq. 

No. 

Hex. 

Bolt 
diam. 
in in. 

No. 

Sq. 

No. 

Hex. 

£ 

7270 

7615 

£ 

280 

309 

l£ 

34 

40 

i 

2350 

3000 

1 

170 

216 

2 

23 

29 

£ 

1120 

1430 

£ 

130 

148 

£ 

19 

21 

f 

640 

740 

£ 

96 

111 

£ 

12 

15 

£ 

380 

450 

£ 

58 

68 

£ 

9 

11 







3 

7.33 

8.5 


Bolts. Approximate Weight per Hundred. Weight of 100 bolts 
in lbs. = a + (b X length in in.). 


Bolt diam. £ 

£ £ 

£ 

£ 

£ 

1 1£ 

1£ 

1£ 

1£ 

Sq. heads 
and nuts. 

a = 2 

5.7 11 

23 

39 

63.6 

97 105 

190 

230 

325 

b =1.4 

3 5.6 

8.4 

12.2 

16.6 

22 30 

35 

40 

50 

Hex. heads 
and nuts. 

a =1.2 

3.7 7 

16 

27 

48 

64 66 

150 

180 

250 

b =1.4 

3 5.6 

8.4 

12.2 

16.6 

22 30 

35 

40 

50 

Bridge Rivets. Weight per 

(6Xlength under head in in.). 

100. 

Weight 

of 100 rivets in 

lbs. 

= a + 

Diam. in in. £ 

£ 

£ 

£ 

£ 

1 

1£ 


1£ 

a =1.8 

5.8 

ll.l 

13.8 

22.7 

38.8 

58.1 


83.6 

b =3.13 

5.55 

8.7 

12.5 

17 

22.25 

28.15 

34.8 


Track Spikes. Number in Keg of 200 Lbs. 

Size. . 4£X£ 5Xrs 5X£ 5X-& 5£X£ 5£X:& 6XA 6X£ 

No... 533 650 520 393 466 384 350 260 


Wire Nails and Spikes. Number in One Pound. 


Size. 

Length 

in. 

Common 

nail. 

Barbed. 

Fine. 

Finish¬ 

ing. 

Barbed 

roof. 

Spikes 

2d 

1 

1200 

876 

1550 

1350 

411 


4 d 

1£ 

432 

357 

760 

584 

165 


6 d 

2 

252 

204 

350 

310 

103 


8 d 

2£ 

132 

99 

190 

170 



10 d 

3 

87 

69 

1S7 

121 


50 

16d 

3£ 

51 

43 


72 


35 

20 d 

4 

35 

31 


54 


26 

30 d 

4£ 

27 

24 


46 


20 

40d 

5 

21 

18 


36 


15 

50 d 

5£ 

15 





12 

60(2 

6 

12 





10 

Spikes: 

6£ in., 

9; 7 in., 7; 

8 in., 5; 

9 in., 4£. 





Lag Screws. Approximate Weight per Hundred. Weight of 100 
lag screws in lbs. —a + (b X length in in.). 


Diam. in in. £ ts £ I £ 

a . 2.2 5.7 8 12 24 

6. . . .. 2.9 3.3 4.6 7.2 10 

Iron Wire. Tensile Strength per Square Inch of Section. 

Diam. in in. 0.05 0.1 0.2 0.3 0.4 

Strength in lbs. 106,000 97,500 87,500 81,000 79,000 

The above for bright, charcoal iron wire. If annealed take 75% of values. 
For Bessemer steel add 10% and for crucible steel 15%. 









16 


MATERIALS. 


Galvanized Iron Wire. 


B & S. 
gauge. 

6 

7 

8 


Lbs. Ohms. 


550 

470 

385 


10 

12.1 

14.1 


B.& S. 
gauge. 
9 
10 
11 


Weight and Resistance per 3Iile 

(Roebling.) 

B.& S 
gauge 
12 

13 

14 


Lbs. Ohms. 


330 

2G8 

216 


16.4 

20 

26 


Lbs. Ohms. 


170 

100 

62 


32.7 

52.8 
91.6 


(Roebling.) 

i 
20 
2.4 


3 

16 

17 


Galvanized Steel-wire Strand (7 wires twisted). 

Diam. of rope, in. ... h rs i fs X 

Wire gauge No. 8 10 11 12 15 

Lbs. per 100 ft. 52 36 29 21 10 b 

Estimated breaking strength in lbs. = 160 X wt. in lbs. of 100 ft. 

Wire Hoisting Rope. (Roebling.) Made from i to 2| in. diam., 6 
strands of 19 wires each, hemp center. Wt. in lbs. per it. — 1.58a . Ap¬ 
prox. breaking strain in lbs. = c<2 2 . 

Diam. in in., d— 1.5 1 

Swedish iron, c = 30,000 32,000 35,000 

Cast steel, c = 60,000 64,000 <0,000 

Transmission or Haulage Rope. 

7 wires each, hemp center. 

Diam. in in., d= 1.5 1 0.5 

Swedish iron, c — 30,000 32,000 33,500 

Cast steel, c = 60,000 64,000 67,000 


& to 1£ in. in diam., 6 strands of 


Extra Strong Crucible Cast-steel Rope (6 strand, hemp center). 

Diam. in in., d = 2.5 1.5 1 „ P;,'X 

19 wire strand, c = 70,000 75,000 <8,000 

7 “ “ c = 70,000 75,000 78,000 

Crane Chains (Pencoyd). Pitch in in. (c. of 1 link to c. of next), 

p" = 0.17 + 2.43d (where d< Jdf in.); 


= 2.75d —0.156 ( 


d>li in.); 


d = diam. of link wire in ins. Outside width of link = 3.3d+jg_ in. approx. 
Approx, wt. per ft. in lbs. - for d = \ to £ in., wt. = 0.8< 54- 6.o(a — t); for 
d = *r to l in., wt. = 2.5 + 14.6(d —4); ford = jto li, wt. = 8 + 21.9(d-£). 
DBG Special Chain. Average breaking strain in lbs. = b2,000dC 

when d fs i in., and 62,000d 2 -6,800(d-|), when d>\ in. For proof test 

take 4 of these values, and for safe load i. Ordinary crane chains have 
from 87 to 90% of the strength of the D B G special chains. Chain sheaves 
should have a diameter of not less than 70d. . 

Holding Power of Nails and Spikes. (Approximate.) korce in lbs. 
required to withdraw nail = cs. ? , where 1 = length of nail in the wood in in., 
and s ^circumference of a round nail or the lour sides of cut nail in in. 


White Pine. 

Wrought spikes, c= 360 
Wire nails, c= 167 

Cut nails, c = 405 


Values of c. 
Yellow Pine. 

318 

662 


White Oak. 

720 

940 

1216 


Weight of Floors. Solid brick arched floors, 70 lbs. per sq. ft. Hollow 
brL'k arched floors, from 20 lbs. per sq. ft. for a 3 ft. span to 60 lbs. for a 
10 ft. spa i. Wooden floors, lbs. per sq. ft. per inch of thickness: White 
Oak, 4; Maple, 3.5; Yellow Pine, 3.2; White Pine and Spruce, 2.33; Hem- 
lock 2 

Floor Loads in lbs. per sq. ft. Street bridges, 80; dwellings, 40; 
churches, t leatres and assembly rooms, 80; grain elevators, 100; ware¬ 
houses, 250; factories, 200 to 400. Prof. L. J. Johnson states as the result 
of experiments that the excessive crowding of adults may produce a load 
as high as 160 lbs. per sq. ft. 1 cu. ft. of brickwork gives a load of 115 lbs. 
per sq. ft. of supporting floor. (Masonry, 160 lbs.) 






MISCELLANEOUS TABLES AND DATA. 


17 


Roof Loads in lbs. per sq. ft. Corrugated iron, 37 to 40; slate, 43 to 46 
(add 10 lbs. if plastered below rafters). These values include an allowance 
of 30 lbs. for wind and snow. Snow per ft. depth, 6.4; maximum wind 

* Brick Masonry. Common bricks are 8£ in.X4^ in. X 2f in. Pressed, 
8* in. X 4$ in. X 2 i in. Wt„ 5 to 6 lbs. Number ot bricks per sq. ft, of 
wall surface = 1.55 Xthickness of wall in inches (approx.). 1,000 closely 
stacked bricks occupy about 56 cu. ft. Safe load lor brickwork in on. 
per sq. ft.: for good lime mortar, 8 tons; for good cement mortar, 15 tons. 

(N. Y. City Law.) 


THE STRENGTH 
STRUCTURES, AND 


OF MATERIALS, 
MACHINE PARTS. 


Stress is the cohesive force within the material which is called into 
action to resist the load or externally applied force. 

Strain is the deformation produced by the stress and is proportional 
to the stress within the elastic limit. 

Elasticity is the property which a body possesses of regaining its orig¬ 
inal shape and dimensions after distortion. 

Modulus of Direct Elasticity. E=~ = ^-. 

O t Oc 

Modulus of Transverse Elasticity. C = f s + d s (for shear). 

Modulus of Volumetric Elasticity. K = f v -r- decrease in vol. per 
cu. in. 

Elastic Moduli (inch and pound units). 


Material. E C K 

Cast Steel. 30,000,000 12,000,000 26,000,000 

Forged Steel. 30,000,000 13,000,000 26,000,000 

Tempered Steel. 36,000,000 14,000,000 

W. I. Bars. 29,000,000 10,500,000 20,000,000 

“ Plates. 26,000,000 14,000,000 20,000,000 

Copper. 12,000,000 24,000,000 

“ rolled. 15,000,000 (fordrawn, E = 17,000,000) 

Cast Iron. 17,000,000 6,300,000 14,000,000 

Brass and Gun Metal. 13,500,000 15,000 000 

Water. ’300^000 


Poisson’s Ratio (M). If a bar be extended or compressed, the direct 
strain ( S t or <? c )=lateral strain (di)XM. The value of M for steel is 3.25, 
for W. I., 3.6, for C. I., 3.7, for copper, 2.6, and for brass, 3. 

Work. The unit of work is one foot-pound. Work = pressure or force 
Xdistance = pounds Xfeet = ft.-lbs., and may be represented by the area 
of a figure with abscissae of distance and ordinates of pressure or force. 
Resilience = the work done in deforming a body up to the elastic limit = 


F 


XA, ft.-lbs. 


total stress in lbs. 


X deflection in feet. 


2 * 2 
Stress Due to Impulsive Load. Make energy equal to the resilience. 
wv 2 FA, , „ ... . wv 2 , . , . 
then, ~2g~~~2' and * (lbs.; = -^r, wllca 1S the maximum. The mean 

total stress (between 0 and max.) 
pile-drivers, etc. 


wv 1 


2 gA, 


which applies to steam-hammers, 


In case of^falling weight (e.g., sudden load on a beam 
or crane chain), w(h + A,,) — — 

Jj 

Stress Caused by Heat. F = Eat°a. 


Coefficients of Linear Expansion (a) per Deg. F. 


Tempered Steel.0000073 

Strong Steel.0000063 

Mild Steel.0000057 

Wrought Iron.0000066 


Cast Iron.0000062 

Brass.0000105 

Copper.0000095 

Bronze.0000111 

18 
























FACTORS OF SAFETY—STRESSES. 


19 


Relative Hardness of Materials. Cast steel, 554 brass 233 mild 
steel 143; aluminum (cast), 103; copper (annealed), 62; zinc (cast), 41 
lead,’4. Strength is increased as the temperature is lowered,-50 to 
100% at —295° F. Iron and steel gam slightly in strength up to oOO r., 
but thereafter the decrease is rapid. 

Factors of Safety. 

Safe Load = Breaking Load -h Factor of Safety. 

^ , T . Moving and 

Dead Live Reversible + 

Load. Load-* Loads. 

W. I and Mild Steel ... 3 5 to 8 9 lo 

Hard Steel. 3 5 to 8 10 to 15 

Bronzes. 5 6 to 9 10 to o 

C. I. and Brass. 4 6 to 10 10 to 15 

Timber 1 j n permanent struc- 

Masonry*^" J . 20to%0 

Herr Wohler’s.ex^rtaente in 187l^howed that rang, of J^atmnjn 

/i= ^_ + V/2-xS/, where ft = the breaking stress under variation, in tons 

highest stress — lowest stress ^ ^ 

S= highest stress 

S = / 1 7for St al?e d rnaSy equli Ensile Td^compVssive stresL^s in shaft! 
ing, S = 2f u whence, for w ^ SteeL 

Steady load. fi = f /l = 0.472/ 

Live load.. n . '/.nor./ 

Reversible load. h 0.33/ 1 i t 

Or, safety factors are in the ratio 1: 2: 3 to 4, approx. 

Average Breaking Stresses of Building Materials. 

(In lbs. per sq. in.) 

Material Tension. Compression. 

White Oak. 10,000 (II to grain) 4.500 (columns< 15Xdtam.) 

La. Long-leaf Pine.' 1^000 “ “ “ 5,000 

Hemp Rope. ’ooo 15,000 

Granite.. : . X . 000 7,000 

Limestone. 150 5,000 

Sandstone. ^ 4 X strength of stone used) . 

Stonework. w B 1 000 (common, in lime mor- 

Brickwork. DU tar) 

300 2,000 (best, in cement) 

Portland Cement/ 1 m. 400 g 

:: Concrete, 1 |00 ^ 


























20 


STRENGTH OF MATERIALS. 


Average Breaking Stresses of Materials and Safe Stresses for 
Ordinary Live Loads, (in lbs. per sq. in.) 


Metals. 


Crucible Cast Steel. 

Mild Steel. 

Structural Steel, 
0.1% Carbon.. . . 

Do., 0.15% C. 

Soft Steel. 

Medium Steel. 

Steel Castings. 

Iron Forgings. 

W. I. Plates || 

“ “ + - 

Cast Iron. 

Malleable Iron. . . . 
Manganese Steel. .. 
Nickel Steel. 

4 4 4 4 

Manganese Bronze 
Phosphor Bronze. . 
Silicon Bronze. . . . 
Aluminum Bronze. 
Delta Metal. 

it 44 

Gun Metal. 

Copper. 

Brass. 

Copper Wire. 

4 « 4 4 

Iron “ . 

4 4 4 4 

steel “ :::::: 

4 4 4 4 

4 4 4 4 

4 4 4 4 


Tension. 

Compression. 

Shear. 

Breaking. 

Safe. 

Break- 

Safe. 

Break- 

Safe. 



mg. 


ing. 


100,000 

18,000 

180,000 

18,000 


11.200 

78,000 

15,500 


15,500 


11,200 

56,000 

11,200 

56,000 

11,200 

48,000 

9,000 

64,000 

12,800 



50,000 

10,000 

52-62,000 

15,000 

(America 

n Bridge 

Webs = 

9,000 

60-70,000 

17,000 

Co. Pract 

ice.) 

4 4 

10,000 

67,000 

11,200 


11,200 


7,800 

56,000 

11,200 

50,000 

9,000 

45,000 

7,800 

50,000 

9,000 


9,000 

36,000 

6,700 

40,000 

9,000 


9,000 

36,000 

6,700 

17,000 

2,800 

100,000 

9,000 

11,000 

2,200 

35,000 

6,000 





135,000 

22,500 

(14% Mn 

) 



83,000 

17,000 

(Plates) 




100,000 

18,000 

(Forging 

s) 



67,000 

11,200 


11,200 


7,800 

56,000 

9,000 


9,000 


6,700 

63,000 

11,200 



67,000 

11,200 





67,000 

11,200 

(Forging 

s) 



45,000 

7,800 

(Cast) 




27,000 

4,500 


4,500 


3,360 

29,000 

4,500 

58,000 

4,500 

25,000 

3,360 

25,000 

3,360 


3,360 


2,200 

36,000 

(anneale 

dL 


60,000 


(unanne 

aled) 



60,000 


(anneale 

d) 



80,000 


(unanne 

aled) 



120,000 


4 4 




80,000 


(anneale 

d) 



180,000 


(crucible 

steel) 



200,000 


(bridge c 

able) 




Note. Where vacancies occur in table, assume compression to equal 
tension, and shear to be 0.7Xtension. || means parallel with grain or fiber, 
+ means across grain. 


Tensile Stress-Action. Load = Total Stress, or rw = /<a, ( = pXarea 
pressed upon in case of steam, air, or water pressure). 

Strength of Chain. w= 14, OOOd 2 lbs. for safe loading, where d = diam. 
in in. of the wire in link. Wt. per ft. = 10d 2 , approx. (See Crane Chains, 

ante.) 

Strength of Ropes, w (safe) = l,120d 2 for White Hemp. For wire 
rope, w (safe) = 20,000n<i 2 lbs., where n = no. of wires and d = diam. of wire 
in in. (See Wire Rope, ante.) 

Strength of Pipes and Cylinders Pressed Internally. 

Thin Cylinders. For a longitudinal section (e.g., boiler) /< = ‘ p —, and 

t 

for a transverse or ring section, ft = ^-. Stresses must be multiplied 

by t) in the case of boilers or other cylinders where "welded, riveted, 
or bolted construction is used. In this case j? = efficiency = strength of 
joint -5-strength of solid plate. For ordinary steam, water, or gas pres- 




































































STRENGTH OF PIPES AND CYLINDERS. 


21 


sures, t = 0.18V / d for pipes and rough cylinders. For machining, in the case 
of cylinders, add 0.3 in. to above value of t. Kent states as an average 
derived from a number of rules: / = 0.0004dp + 0.3 in. 

Thick Cylinders. (For ve ry h igh pr essu res, e.g., hydraulic.) Exter¬ 
nal diam. = Internal diam. X V/, + p -j- v/, — p. 


Tensile Stress induced by Centrifugal Force. f t = 


12wv 2 


For cast 


For steam cylinders, etc., No. of bolts = ; 

shanks should 


iron w> = 0.261 lb. and ft safe = 2,800 lb. Placing these values in formula, 
v is found to be 170 ft. per sec., or the safe theoretical velocity of a fly¬ 
wheel rim (double actual practice). 

Strength of Bolts. The working stress per sq. in. of cross-section at 
the bottom of thread for ordinary joints = 8,000 lbs. for W. I., and 11,000 
lbs. for mild steel. (If under steam or water pressure, 6,000 lbs. In this 
case boltsin. should not be used and the pitch should not exceed 6 cl.) 

+ Where bolts 

2400 Vbolt diam./ 

have to resist shock the shanks should be turned down to the diam. at 
bottom of thread. _ 

Compressive Stress-Action. w = / c a. (Applicable where length<12a.) 
(See Columns.) 

Shear Stress-Action. For pins and rivets, w = f g a. f s safe = 11,000 lbs. 
per sq. in. (Am. Bridge Co. practice.) 

Strength of Eye Bars, ft safe = 14,000 to 16,000 lb. for soft and me¬ 
dium steel respectively. . . 

Proportions: D — d = lAb\ d = $ to \\b] t (for&<5 in.) = 0.75 in.; t (for 
fc>5 in.) = (6 + l)-j-8 (in.) Radius of fillet at neck = D = outside diam. 
(Passaic R. M. Co.) b = d = 0AD. Fillet radius = D. (Shaler Smith.) 

Strength of Riveted Joints.—Single-riveted Lap Joint. Shear 
strength of one rivet = tensile strength of plate between two holes, or 
/ 8 ^rf 2 -5-4 = /<(p"-d)f (1). d (of rivet) = 1.2 before riveting; d = di (of 
hole) = 1.3v7 after riveting (for plates in.). Substituting in (1) and 
making /„= 11,200, /, = 13,500, pitch, p" = 1.09 + di for steel. For iron 
plates and rivets p" = 1.14 +d x ; for steel plates and iron rivets, p = 0.76 + 
di; for copper plates and rivets p = 0.98 + di. (Supplee gives as standard 
practice (up to i in. plates) 1.31 and 1.25 in place of 1.14 and 0./6 as above .) 
Center of rivet to edge of plate = i overlap = 1.5rf. r .. 

Double-riveted Lap Joint (s taggered or z igzag), p = 2.18 + di. ins¬ 
tance between rows of rivets = Vi.OQdi + 0.75di 2 . 

Chain-riveted Lap Joint (double riveted, but not staggered;, p — 
2.18 +d\. Distance between rows = 1.5 + c?i. 

Double-riveted Butt Joint (with two cover plates), p =4.36 + rfi. 
Diagonal distance between centers of rivets in the two rows = 2.18 +di. 
Thickness of each butt strap or cover plate = |< of plate. Overlap -2d. 

Treble-riveted Butt Joint. This case calls for three rows of rivets. 
The pitch of the third row from edge is twice the pitch of the hrst two 
rows which are staggered Examining as a lap joint the metal between 

0 655a 2 

two holes on pitch line = (p" - d) = = the strength of one rivet. 

3.275<fi 2 

As 5 rivets have to be taken care of, then p" = ——:-bdi. Considered 


t 


as a butt joint, ( p" — d ) = 


1.31d 2 
: t ’ 


and for 5 rivets, p' 


6.55di 2 
t 


+ d\. An 


intermediate value is generally taken. . (p —pitch of third row ftom edge 
of plate.) In the above formulas p" is taken equal to di plus 2.18, 4.36, 
etc., which are multiples of 1.09 in formula for^ single-riveted lap joint, 

and are for steel plates and rivets where = 13 ^ 00 1 For other metals or 

combinations similar multiples of 1 14, 0.76 0.98, etc., should be used, 
or, if other safe stresses are chosen for fa and ft, values of p . should be 
worked out from formula (1). Overlap —1^ to 2d for treble-riveted butt 
joint, thickness of butt strap = of plate. 

Rivet Proportions. 


LcLyJ — gt # 

Round or snap head: large diam. —1.67Xrivet 












22 


STRENGTH OF MATERIALS. 


diam, and height of head = id. Countersunk head: large diam. = lfd, 
and is coned to rivet shank at an angle of 60°. 

Efficiency of Joints. jj = -— 77 ^. (Following table gives 15 for steel 

'P 

where /*-*-/« = 1 . 2 .) 


t. 

d. 

Single-riv. 

Lap. 

Double-riv. 

Lap. 

Double-riv. 

Butt. 

Treble-riv. 

Butt. 

1 

i 

.57 

.73 

.84 

.93 

J 

i 

.54 

.70 

.82 

.92 

i 

ItV 

.49 

.66 

.79 

.90 

1 

li 

.45 

.62 

.77 

.90 

H 

H 

.40 

.57 

.73 

.87 


Riveting in Structural Work (example,—plate girder). Flange area 

a =—r. Bm (neglecting bending stress on web) =ahf (1). Bm of web = 

hf 

fth 2 . fth 2 

——-, or allowing for rivet holes, =- 5 -, and Bm (considering bending stress 
o o 


on w^eb ) = hj(a + ^), and the flange area a = ^ ( 2 ). 

Riveting: Lower angles to web (in tension), neglecting Moment of 
Resistance of web to bending; pitch of rivets, p" = /i/s-r- V, or the vertical 
shear. Upper angles to web, compression, M. of R. neglected; p" = 



1 

V 2 + h 2 w 2 ’ 


where w — total loading 


per inch of length. 


p", h, t in in., 


a in sq. in., fs ( = least strength of rivet subject to double shear and bear¬ 
ing stress) in lbs. per sq. in., V and w in lbs. 

The pitch of rivets joining flange plates to angles is 6 in., excepting at 
and near the ends of flanges, where p" = 4d. 

Web stiffeners are angles riveted vertically to the web to prevent buck¬ 
ling of the latter. If i< — the stiffeners shoulc^ be spaced h in. apart 
(maximum spacing = 60 in.). 

Pins, bolts, and rivets, unless fitting tightly and thoroughly gripping 
the plates, will be subject to bending stresses and smaller unit stresses 
must be employed, viz.: for circular sections, 0.75 f S ] for square sections, 
0.66/g; for square sections, forces acting along diagonal, 0.89/ s . 

Strength of Cotter Joints. d = diam. of rod = breadth of cotter mid¬ 
way between ends = 4 X thickness of cotter. Taper of cotter 1 in 30 to 
1 in 100. If tapered much greater than 1 in 30, cotters are apt to fly out. 

Torsional Stress-Action. External Moment = Moment of Resistance 


at section, or wr — jgSt. 

Strength of Round Shafts. Moment of Resistance of section = 

/ 7)4 _// 4 \ 

0.1964/ s d 3 for solid shafts and 0.1964 / s (^———J for hollow shafts. 


Strength of Square Shafts. Moment of Resistance of section = 
0.208/sS 3 , where s = side of square in in. 

Factor of Safety for Stiffness = 10 for short shafts; 16 for long shafts. 
Strength of Flange Coupling Bolts. 


Diam. of bolt = 0.577''/(diam. of shaft) 3 -^ (bolt circle radius X No. of bolts). 

Strength of Sunk Keys. (Average practice.) Breadth = A (diam. 
of shaft) + T 6 in.; Depth = i (diam. shaft) + | in.; Length = 0.3 (diam. 
shaft ) 2 -h depth. For splines or keys upon which parts rotating with shaft 
may also slide axially, interchange the above dimensions for breadth and 
depth. 

The Angle of Torsion, (d), is the angle through which one end of a 
shaft turns relatively to the other end under a given stress. (0 = arc -s- radius.) 

0 = 2 f 3 l -r-(dX Modulus of transverse elasticity, C ). 

Strength of Helical Springs. For round wire, using shaft equation. 

rd 3 ... 

wr = f8hr, where w — axial pull in lbs., r = radius of coil (to center of wire 
16 








CONICAL SPRINGS. BENDING STRESS. 


23 


section), f a (safe) — 60,000 (Begtrup and Hartnell). For square wire, 
wr .~ 0—08/gs . Deflection = 2f s lr-+-Cd, where / = 2xrXNo. of turns or 
spirals n; d — diam. of wire, and C = 12,000,000. All dimensions in in. 

I'lirther, deflection = 64wnr :i -s- Cd 4 for round-wire springs, and = 
60 .ownr . Cs for square-wire. (Falues of fa and C are for steel wire.) 

jo r ' 

Conical Springs, round wire, = where r = largest radius of coil. 

^ 16wnr 3 

Deflection =————. 

Cd 4 

Flat volute (rectangular section of height h, breadth or thickness b), 

wr = 0.222b 2 hfa. Deflection = 1 - 8nWnr ^ b2 + h2 ) 

Cb 3 h 3 

Spiral Springs in Torsion. 

Round wire, wr = nf s d 3 +32. Deflection at r = 64wlr2 , 

izEd 4 

Square wire, wr = f s s 3 -t-6. * 4 “ r = * ~ w Ill 

Es 4 

(l = developed length of spring in inches.) 

Bending Stress-Action. In an overhung beam, or cantilever, the 
upper fibers are in a state of tension and the lower ones in compression, 
while in a supported beam, or girder, the opposite is the case. There 
exists therefore an intermediate longitudinal section where these stresses 
are zero in value. The intersection of this longitudinal section and a 
vertical cross-section is a line called the Neutral Axis, which passes through 
the center of figure (or gravity) of the cross-section. Consider two small 
areas, a t and a c (distant y t and y c from neutral axis), and let p be the radius 
of curvature of the neutral longitudinal section of the beam when under 
bending stress. Then, assuming the beam or bar to be bent into a cir¬ 
cular ring, l of bar (before bending )*=2np; l (after bending), or circum¬ 
ference of bar at area at = 2n(p+ yt), in tension, and l at area a c = 2it{p — y c ), 
in compression. Consequently, the strain on fibers at at = 2 tz(p + yt)~ 

2np = 2nyt, and strain at a c = 2np — 27i(p — y c ) = 27:yc; but J generally; 

hi 

.*. 2tty — ^ —\^ P and /=— ( 1 ), and the total stress on a small area a, 

th p 

= /a-S«. 

P 

Moment of Resistance. Moment of stress on the small area a = 
fay = ^y~, and the moment of all stresses on the section =—Iay 2 . Iay 2 = 

P p 

Moment of Inertia of the section (or Second Moment) = 7. .*. Moment of 

El 

Resistance = — (2). Representing the moment in terms of the limiting 

P 

stress, then. Bending Moment, 7?»n = /5 = Moment of Resistance (3). S is 
called the Section Modulus (= virtual area X arm through which it acts). 

From (1), (2), and (3), S = —, and Bm = —. 

y y 

Moments of Inertia of Area. 

For Beams. 

Section. 7. y ( = dist. of furthest fiber 

Rectangle, axis || to breadth and from axis.) 

.. . . bh* h 

bisecting section. — — 

„ . h 4 h 

Square, ditto, ( b—h) . -77 

Square, axis bisecting section on _ 

s 4 2 

diagonal. jTj —(s = side of square.) 











24 


STRENGTH OF MATERIALS 


Hollow rectangle or square, axis 
as for rectangle above. 

Triangle, axis || to base. 

Circle, diameter as axis. 

Hollow circle. 


bih\ 3 — bh s 
12 
bh 3 
36 

nd 4 

64 


n 

64 


W-d 4 ) 


hi 

2 

2 h 
3 
d_ 

2 

(&i, hi, and d\ are outer 
dimensions.) 


For shafts. (Polar Moment of Inertia = /?.) 

Section. Ip. y. 


Rectangle 


bh(b 2 + h 2 ) V b 2 + h 2 
12 2 


Square 

Circle. 


~ «-*-V2'=o.707« 

6 

nd 4 d 

~32 ~2 


Hollow circle. ^~ IT (di = outer diam.) 

The Polar Moment of Inertia 7p = 7 + 7j, where 7 and 7i are two Moments 
of Inertia of the section which are taken at right angles to each other through 
the c. of g. of the section. _ 

The Radius of Gyration, r = V - - -t—. 

area of section 


Moment of Resistance. Graphic Solution. .47? is the neutral axis 

of the rectangular section CDHJ, and 


l*-b - - 

I 



CD the line of limiting or greatest 
stress. The Value of any horizontal 
fiber EF to resist stress is found by 
projecting the same vertically to the 
line CD and joining C and D to N. 
The intercept GM is the value de¬ 
sired. All fibers being thus treated, 
the sum of the virtual stress areas 
will be the areas CDN and 77 JN 
which each make one force of the 
couple when multiplied by the limit¬ 
ing stress /. K and L are the cen¬ 
ters of gravity of the areas. 

Moment of Resistance of rectan¬ 
gular section = / (area CDN or HJN) 

Xarm KL = }\—) X — = /— = !$■ 

Moment of Inertia of any Sec¬ 
tion. Find fS by above method, 
divide by value of / and multiply 
by y. (7 = Sy.) For rectangular sec- 
. c bh 2 h bh 3 

tion, <S = —, y—r —, and 1=^2' 


Center of Gravity and Moment of Inertia Determined Graphic¬ 
ally (Fig. 3). Beam section 1 2 3 4 5 6 ... 12. To find center of grav¬ 
ity (considering right half of section): Project each horizontal fiber of 
section vertically to the arbitrarily assumed line x\Xy parallel to base line xx. 
Join ends of projection to point b and note the intercept on each fiber. 
The sum of all these fiber intercepts will be the area a 24 17 16 25 26 b a, 
or A\. Then, Ayh=*AG, where A is area of right half of section (sufficient 
in case of symmetry) and G = distance of center of gravity from xx. Then, 
G = A\h-r-A, which determines the position of neutral axis, zz. 


























MOMENT OF INERTIA. 


25 


To find 7 of the section around 2 ? (considering left half of section) Project 
every horizontal fiber strip of section to ll, the line of limiting stress, join 
ends of projection to point c (center of gravity) producing if necessary ■until 
1 he original strip is crossed, and note the intercepts. The areas 1 a c 14 13 1 
(«,) and c IS 23 22 b c (of) are thus found, and on opposite sides.of verti¬ 
cal center line. They are the 1st moments. Go through the same process 
as above with the areas 01 and of, and the second moment areas 1 a c 15 14 1 



(an) and cb 21 20 19 c (a 2 0 will be obtained, both being on the same side 
of vertical lhie. Then (doubling the results for the entire section), / = 

2(a 2 + a 2 ')y 2 and S =—=2(a 2 + a 2 ')y. In cast-iron beams if /«“>/*. then /* 

is the limiting stress and the line ll should be drawn at a distance yt from 

ne positfon of Center of Gravity. The centers of gravity of regular 
figures (plane or solid) are the same as their geometrical centers. 

Triangle: i distance from middle of side to vertex of opposite angle. 


























26 


STRENGTH OF MATERIALS. 


Trapezoid: divide into two triangles by a diagonal and join their centers 
of gravity; repeat process with the other diagonal and the intersection of 
the lines joining the centers of gravity will be c. of g. of trapezoid. 

Sector of circle: on radius bisecting the arc, distance from center = 
(2 Xchord X radius) h-( 3 Xlength of arc). 

Semicircle: on middle radius, 0.4244r from center. 

Quadrant: on middle radius, 0.G002r from center. 

Segment of circle: distance from center = (chord) 3 -^(12Xarea). 

Parabola: g length from vertex, and on axis. 

Semi-parabola: £ length from vertex, f semi-base from axis. 

Cone, Pyramid: in axis, i its length from base. 

Paraboloid: in axis, § its length from vertex. _ 

v h IA +3a + 2v / A< 

Frustum of Pyramid: distance from larger base = — 1- 


Frustum of Cone: 


= — ( ; 
A \ 


A + ^A 
77 2 +r( 2/2 + 3^ 


4a\ 

a/* 


)• 


4 v R~-n\R, J t-rj 

h — height; A, a, and R,r = larger and smaller base areas and radii respec- 
tively. 

Two or more bodies in the same plane: refer to co-ordinate axes. Mul¬ 
tiply the weight of each body by the distance from its center of gravity to 
one of the axes, add the products and divide by the sum of the weights, 
the result being the distance of the center of gravity of the system from 
that axis. If bodies are not in a plane, refer them similarly to three rect¬ 
angular planes. 

Moment of Inertia of Compound Shapes. The Moment of Inertia 
of any section about any axis = the Moment of Inertia about a parallel axis 
passing through its center of gravity+ [area of section X (distance between 
axes) 2 ]. Also, the Radius of Gyration for any section around an axis par¬ 
all el to another axis through the center of gravity = _ 

(dist. between axes) 2 + (radius of gyration around axis through c. of g.) 2 . 

By these rules the 7 and r of “built up” beams and columns may be ob¬ 
tained,—-for 7, by finding the 7 of the several components of section about 
the same axis and adding the results for the combined section. 

Bending Moment and Deflection of Beams pf Uniform Section. 

(W = total load on beam.) 

I. Beam fixed at one end, concentrated load at the other. Maximum 
B m at fixed end = Wl. ( B m may be represented by the ordinates of a 

Wl 3 

right-angled triangle having base = / and height = TEZ.) Deflection = r-r—. 

• oHjI 

II. Beam fixed at one end, uniformly distributed load (e.g., wt. of beam). 

Wl 

Max. B m at fixed end = -^-. ( B m represented by ordinates from base of 

length l to a semi-parabolic curve having vertex at free end of l and axis 

l \ Wl 3 

perpendicular thereto, and whose semi-parameter = ). Deflection = 

III. Beam, ends supported, concentrated load at tenter. Max. B m at 

Wl . Wl 3 

center — —r. Deflection == „. ■. 

4 48E7 

IV. Beam, ends supported, concentrated load at any point. Max. Bm = 
W(l — x )x 

--—, where x = distance of load from one support. Deflection = 

Wx 2 {l — x) 2 
3 EH ’ 

V. Beam, ends supported, uniform load. 

5W1 3 
Deflection = • 

VI. Beam fixed at both ends, centrally loaded. Max. Bm at center and 

Wl . IE/ 3 l 

8nds = -x-. Deflection = Points of contra-flexure distant — from 

o aili 4 

ends. 

VII. Beam fixed at both ends, uniformly loaded. Max Bm at ends== 


Max. Bm at center = 


Wl 

IT* 












STRENGTH AND DEFLECTION OF BEAMS. 


27 


Wl 

12 


- ( 
91 ’ V 


Wl_ 

24 


r )- 


TFZ 3 

at center;. Deflection = 55 - 7 ^ 7 . 

ooQtJtLl 


Points of contra-flexure are 


0.21 H from ends. 

\ III. Beam fixed at one end, supported at the other and uniformly 

loaded. Max. B m at fixed end = — 5 -, Deflection = Point of con- 

^ o y^ozw 

tra-flexure = -^- from fixed end. 

IX. Beam fixed at one end, supported at the other, and centrally loaded. 

Section 

X. Beam loaded at each end with —, with two supports, each distant x 

from ends. Max. B m = Deflection, overhang, = ^ ^ X \ for 


middle part, = 


Wx(l-2x)2 


12EI 


16 El ‘ 

XI. Beam, both ends supported, with two symmetrically placed loads 

/ W \ . Wx 

^each = — j, each x dist. from support. Max. B m = —^~. Deflection => 

Wx(3P-4x2) 

4SEI ‘ 

XII. Beam, fixed at one end, distributed load increasing uniformly from 

, „ 117 TT73 

Q towards fixed end. Max. B m = —. Deflection = 

o loEl 



XIII. Beam, both ends supported, distributed load increasing uniformly 

Wl 31 vi 3 

from 0 at center towards ends. Max. B m = ——. Deflection = xx>rvr,-. 

I* oZOrLl 

XIV. Same as XIII, but with load increasing uniformly from O at ends 

Wl . Wl 3 

to center. Max. B m = ~^-. Deflection = qq^j- 














































28 


STRENGTH OF MATERIALS. 


XV. Beam overhanging each of two supports by distance x, uniformly 

\y r 2 W 

distributed load. B m = — - at either support, and —(x —0.25 1) at center. 

3 Wl 

Max. B m (when x = 0.2071) = . 

Combinations of loading may be shown graphically as in Fig. 4. W = 
uniform load, and W\ = concentrated load. Consider the beam as merely 
supported at the ends, with a uniform load (e.g., itself). Then, the par- 

Wl 

abola AFB, on base AB, and of height = - 3 ~, is the curve of 5m for IF. 

O 

Again, consider beam as loaded only with TFj. Then, the triangle AGB 
will be the curve of Bm. for Wj, and, by adding the ordinates of these curves 
a new curve AHEIB is obtained, which is the curve of B m for the com¬ 
bined loads on a freely supported beam. Again, consider the beam as 
fixed. The Bm of the supported beam is now opposed by the reaction 
of the wall, which is a constant strain and whose Bm curve is the rectangle 
ACDB, equal in area to AHEIB. The algebraic sum of these bending 
moments gives for the fixed beam the shaded Bm curve ACHEIDBIHA, 
and the intersections at H and / determine the points of contra-flexure. 
The portions CH and ID are strained as cantilevers, the upper sides 
being in tension, while the part HI is strained as a supported girder, with 
tension on lower side. # ... 

The B m curve for a moving load (e.g..that on a travelling-crane girder) is 

Wl 

parabolic, with a maximum at center equal co ——. 

Shear Stresses. The vertical shear stress caused by a concentrated 
load is represented by the ordinates of a rectangular area having a length = 
dist. from point of support to point of max. B m , and a height = reaction 
at point of support. The vert, shear stress caused by a uniformly dis¬ 
tributed load is represented by the ordinates of a right-angled triangular 
area having base as above, and height at point of supnort = reaction at 

that point. Thus, in Fig. 5, 
rectangles 1 2 3 4 and 2 5 6 7 
15 are for concentrated load W% 
(see Fig. 4), and triangles 
18 9 and 9 10 7 for distrib- 
10 uted load W. The algebraic 
sum of these areas gives areas 
1 11 12 and 12 13 14 15 7 12, 
any ordinate of which shows 
the vertical shear stress of the 
combined loads at the point 
, where ordinate is erected. 

6 Heights 14, 6 7 and 1 11, 
7 15 represent the reactions 
n or proportions of Wi and W 
respectively sustained by the 
points of support. 

Horizontal shear stress. 
If a summation of the hori¬ 
zontal forces (tensile and com¬ 
pressive) is taken, proceeding 
from the upper or lower fibre 
to the neutral axis, it will be 
found that, the max. hor. shear 
stress is at the neutral axis, 
and, in a rectangular beam, at 
any section: Max. hor. shear 
stress =. (3 X Vert, shear at 
the section considered) -5- 2bd, 
where b and d are breadth and depth of beam. In long beams the shear 
is small compared with the bending stress and is fully taken care of by the 
surplus section; in short beams it should be considered. 

Continuous Beams. (Reactions on supports in terms of Wi , the uni¬ 
form load on each span.) 










COMBINED STRESSES. 


2V) 


3 supports 

4 

5 

6 

7 

8 
9 

10 


3 

4 
11 
15 
41 
56 

152 

209 


10 

3 








11 

11 

4 







32 

26 

32 

11 






43 

37 

37 

43 

15 





118 

108 

106 

108 

118 

41 




161 

137 

143 

143 

137 

161 

56 



440 

374 

392 

386 

392 

374 

440 

152 


601 

511 

535 

529 

529 

535 

511 

601 

209 


each X IF. -=- 8 

“ “ -s- 10 

“ “ -s- 28 

“ “ 38 

“ “ -f-104 

“ “ -*-142 

“ 4 h- 388 

“ “ -=-530 


1 Tr! 1e n^r 11 f? W r!f ble D ? flec 1 i( ? n for cantilevers is B \, in. per foot of span, and 
so in. per tt. of span for girders. 


hrSdth l *h° f , U, j! forn ? strength (Rectangular Section).—With constant 

tex at h.a^d^rf h TT ne + th i e of1 l ' a semi-parabola with ver- 

k i aded e /> d ' 11 ’ a triangle, base at fixed end; III and IV, two semi- 

fni° a w^ rtlCeS + at stJPPo rts, bases i° in ing at load point; V, a semi- 
triSfS’A w? C ? n | tan ] t de P th T the breadth varies as the ordinates of; I, a 

? n f e ’ base at Axed end; II, distance between two convex parabolas 
noint v’ r £ ° UC t at free end; III and IV, two triangles, bases at load 
f> t. V, distance between two symmetrical concave parabolas intersect- 
+ 0 O1 i, ts ¥ support- (I, II, III, etc., refer to conditions of loading 
under the heading of Bending Moment and Deflection of Beams, ante.) 

Strength of Circular Flat Plates of Radius r (Grashof).—Plate sup¬ 
ported at circumference and uniformly loaded; /=0,833pr‘ -=-* 2 . Same load¬ 
ing, plate fixed at circumference: f=0.666pr2-*-<* Plate supported at cir¬ 
cumference, loaded centrally with w (of radiusn): /= (l.333 log — + l) —. 

Strength of Square and Rectangular Flat Plates, Uniformly Loaded 

(Unwin).—Rectangular plate, fixed at edges: / = 0 . 5 & 2 p pH -(&4 + m« wdiere 
i JTr?o e r adt . it nd length of plate in in. Square plate, fixed at edges: 

ooa iS ’ , w ‘ lere s —side in in. Surface supported by stays: / = 
v.-j-,Zps . /-, where s = distance in in, between the centers of stays, which 
are arranged in row\s. /--working stress in lbs. 

Strength of I* lat Stayed Surfaces, (See Steam Boilers.) 

Strength of Laminated Steel Springs, w = 


6 1 


Deflection, 4 = ~ 

hit 


T vd ?, er< L tf \. max -. static load on one end of a semi-elliptic, or \ max. load on 
lull elliptic spring; / = allowable stress in lbs. per sq. in. (varying accord- 

lng . 7 °tnr? g T ty and temper) = 90,000 for i-in. plates, 80,000 for 1-in., 
and 75,000 for i-in.; n = no. of plates; Z = half span in ins.; £’ = 30,000,000. 
(Reuleaux and Gaines.) 

Combined Stresses. 

Bending and Tension (Load parallel to axis at distance r).—Bending 
action — wr — f r S — ftcS-, tensile action = w = f t a. Combined max. tensile 

stress on edge nearest axis of w=ft=w(- —h—(See Modulus of Rup- 

. ' CaO/ 

ture.) 

Strength of Crane Hooks. w = abf t -^-C, where a = radius of inside 
ol nook or sling, h== breadth of hook on hor. section through center of inside 
e ’ " = thickness of section, w = load in lbs., /, safe = 13,000 to 

i/,000 lbs. 

Values of <7: 


Rectangular section. 

h-i~a= 1 

1.5 

2 

2.5 

3 

4 

<7=12.6 

7.25 

5.07 

3.92 

3 22 

2 41 

Trapezoidal section. 

<7= 15 

8.96 

6.42 

5.06 

4.18 

3.28 

Elliptical “ 

(7 = 21.5 

12.58 

8.89 

6.92 

5.73 

Distance from center of hook circle to shoulder on 

bolt end = 2 h. 

Diam. 


of bolt end di — ^j~ 267 * trapezoidal sections, the wide edge b should 

be next to rope or chain; narrow edge bi = b -*- + 1). 

(Ing. Taschenbuch). 


w 






































30 


STRENGTH OF MATERIALS. 


Towne eives the following proportions: Neck = d (taken as unit): turned 

Reuleaux gives the following; 2a - KtXwldth 2 ^ d hook 

»US2. ".fte Taschenbuch formulas 

(taking ft = 13,000). ^Compare with formula /*-«>( a + <s )') 

Bending and Compression. Substitute fc for U in formulas for bend- 

in 8 C^r s T„d K e >® \& l * r ca-J-olv^bending and 


Gordon’s Formulas. / breaking = 


72 

1 + b-o 


, both ends fixed or flat; 


a 


one end fixed, other 


1 +1.8&(g)’ hinged or round; 


a 


l+4!-(|)’ roum!; 


, both ends hinged or 


where l=length in ins., least radius of gyration, and a and b are as 

follows: , 

Clm O* 

Cast Iron . 80,000 q^qq 

W. I. and very soft steel.. 36,000-40,000 „„ to 


Medium Steel. 
Hard Steel.... 
Dry Timber... 
Soft Steel.*.... 
Medium Steel. 

Then, w (lbs.) 


67,000 

114,000 

7,200 

15,000 

17,000 


36,000 

1 

22.400 

1 

14.400 

1 

3,000 

1 

13,500 

1 


40,000 


Am. Bridge Co. Practice. 

Safe values. 


11,000 _ 

f (breakin g) in lbs, per sq. in. X area of section in sq. in. 

Factor of safety. 


For W. I. and steel, factor of safety = 4 for dead load, and 5 for moving 
load. For C. I. not less than 8. . j ~ , , r , 

Prof. Lanza states as the result of experiments that Gordon s iormulas 
do not apply in the case of cast-iron columns, and he recommends 5,000 
lbs. r>er sq. in. as the highest allowable safe loading, the length of column 
not to exceed 20 times its diameter and the metal to be of thickness suffi¬ 
cient to insure sound castings. , , , , , 

Eccentric Loading. When the resultant of the load does not pass 
through the c. of g. of the section, let r= distance between resultant and 
c. of g. of section; I its moment of inertia about an axis in its plane pass¬ 
ing through the c. of g. and perpendicular to r; y = distance between said 
axis and fibre under greatest compression; w = total pressure on section. 

Then /= — Assume a section, compute /, and if it exceeds safe 

value (5,000 for C. I.) assume another section and compute / until a safe 























CARNEGIE ROLLED STRUCTURAL STEEL. 


31 


value is found. Eccentric loading in buildings is due to the unequal dis 

Sftffl! persq^in. for at ‘° ° C0Ur ° nly in rare 

Safe Loads for Round and Square Cast Iron Columns. (City 
Building Laws, 1897.) Safe load in tons of 2,000 lb ~ - Ca 

1 + TT2 

C (round or sq.).. N ?" Y f k ' Chic | go ' 

b (square).=500 1,067 800 

6 (round).=400 800 600 

unrfef'ltom B°oile”°" OW C5 ' llnd<!rs «® (See Furnace Flues 

Bending. This combination of stresses exists to a greater 
or less extent in all shafting. Equivale nt twisting moment = 2Xequiva- 

I /^ t =^ dingmoment = ^ + V5 ^ 2 + T m 2 . where T m = twisting moment = 

Torsion and Compression. (Propeller shaft.) — Tm2 % a 

safety factor of 5 should be used. ^ 

formS?a U ?n hrlff UptUre ,* m T he ult i m ^ e s £ esa obtained from the momental 
breaking a solid beam by bending will usually be found much 
greater than f t breaking. Modulus of Rupture f r = cf t , where c generally = 2 
for circular and square (one diagonal vertical) sections, 1.5 for squareand 
rectangular sections, and unity for I and T sections. The values of c 

& n 7 h fI e i Ver p?i, h ' material: Rectangular sections; Fir, 0.52 to 0.94; 
y a *, 0.7 to 1; Pitch-pine, 0.8 to 2.2; C. I., 2; W. I., 1 6- Forced steel 
l- 47 ,; Gun metal, 1. Circular sections: C. I., 2.35* W i’ 175^ Forced' 
steel, L6; Gun metal, 1.9. I sections: C. L,’1+(web’thick ness/flange 

CARNEGIE ROLLED STRUCTURAL STEEL. 

^ In the following tables, w = weight in lbs. per lineal foot, a = area of sec¬ 
tion in sq. in., A-depth of beam or channel in in., 6 = width of flange in 
xn., t = thickness of web m m. & 

*• Xu *2 = distance between c. of g. of section and (1) outside of channel web: 

7 r ?=lfim U f d r° flange on T; (3) back of flange of equal leg angle. 

7, r, o Moment of inertia, radius of gyration and section modulus, where 
.Neutral axis is perpendicular to web at center (Beams and chan- 
nels). 

.« .*.* Parallel to longer flange (Unequal leg angles). 

through c. of g. parallel to flange (Ts and equal leg 
it angles). 

ti nr x j?.'* through c. of g. perpendicular to web (Zs). 

* »* Moment of inertia and radius of gyration, where 

Neutral axis is coincident with center line of web (Beams). 

«. << <• Parallel to center line of web (Channels). 

,, ,, .... . shorter flange (Unequal leg angles), 

through c. of g. coincident with stem (Ts). 

“ “ “ “ • “ web (Zs). 

r ^~Least radius of gyration, neutral axis diagonal, 
o —Section modulus, where 

Neutral axis is through c. of g. coincident with stem (Ts). 

44 4444 , web (Zs). 

si rn a: • ± r parallel to shorter flange (Unequal leg angles). 

C = Coefficient of strength for fibre stress of 16,000 lbs. per sq. in. for 
beams, channels, and Zs, and 12,000 lbs. per sq. in. for Ts. 

11 L = 84/ = .where /= 12,000 to 16,000 lbs.; M = moment of forces 

in ft.-lbs., TF = safe uniformly distributed load in lbs., L = span in feet. 
Cor concentrated load at middle of span use one-half the value of C in the 
tables. For quiescent loads /= 16,000 lbs. per sq. in.; for moving loads, 
12^00 lbs., and, if impact is considerable, / = 8.000 lbs. 

For columns or struts consisting of two latticed channels, r of column 
section (neut. axis in center of section || to webs) = distance between c of g 










32 


STRENGTH OF MATERIALS 


of channel and center of column section (neglecting the la of channels 
around their own axes,—a slight error on the safe side). 

Carnegie Steel I Beams. 

(Sizes with * prefixed are standard, others are special.) 


h. 

w. 

a. 

t. 

6 . 

I. 


r. 

r'. 

S. 

24 in 

100 

29.41 

0.75 

7.25 

2380.3 

18.56 

9 

1.28 

198.4 


95 

27.94 

.69 

7.19 

2309.6 

47.1 

9.09 

1.3 

192.5 


90 

26.47 

.63 

7.13 

2239.1 

45.7 

9.2 

1.31 

186.6 


85 

25 

.57 

7.07 

2168.6 

44.35 

9.31 

1.33 

180.7 

* 

80 

23.32 

.50 

7 

2087.9 

42.86 

9.46 

1.36 

174 

20 

100 

29.41 

.88 

7.28 

1655.8 

52.65 

7.5 

1.34 

165.6 


95 

27.94 

.81 

7.21 

1606.8 

50.78 

7.58 

1.35 

160.7 


90 

26.47 

.74 

7.14 

1557.8 

48.98 

7.67 

1.36 

155.8 


85 

25 

.66 

7.06 

1508.7 

47.25 

7.77 

1.37 

150 9 

* 

80 

23.73 

.60 

7 

1466.5 

45.81 

7.86 

1.39 

146.7 


75 

22.06 

.65 

6.40 

1268.9 

30.25 

7.58 

1.17 

126.9 


70 

20.59 

.58 

6.32 

1219.9 

29.04 

7.7 

1.19 

122 

* 

65 

19.08 

.50 

6.25 

1169.6 

27.86 

7.83 

1.21 

117 • 

28 

70 

20.59 

.72 

6.26 

921.3 

24.62 

6.69 

1.09 

102.4 


65 

19.12 

.64 

6.18 

881.5 

23.47 

6.79 

1.11 

97.9 


60 

17.65 

.56 

6.09 

841.8 

22.38 

6.91 

1.13 

93.5 

* 

55 

15.93 

.46 

6 

795.6 

21.19 

7.07 

1.15 

88.4 

15 

100 

29.41 

1.18 

6.77 

900.5 

50.98 

5.53 

1.31 

120.1 


95 

27.94 

1.09 

6.68 

872.9 

48.37 

5.59 

1.32 

116.4 


90 

26.47 

.99 

6.58 

845.4 

45.91 

5.65 

1.32 

112.7 


85 

25 

. S9 

6.48 

817.8 

43.57 

5.72 

1.32 

109 

* 

80 

23.81 

.81 

6.4 

795.5 

41.76 

5.78 

1.32 

106.1 


75 

22.06 

.88 

6.29 

691.2 

30.68 

5.60 

1.18 

92.2 


70 

20.59 

.78 

6.19 

663.6 

29 

5.68 

1.19 

88.5 


65 

19.12 

.69 

6.1 

636 

27.42 

5.77 

1.2 

84.8 

* 

60 

17.67 

.59 

6 

609 

25.96 

5.87 

1.21 

81.2 


55 

16.18 

.66 

5.75 

511 

17.06 

5.62 

1.02 

68.1 


50 

14.71 

.56 

5.65 

483.4 

16.04 

5.73 

1.04 

64.5 


45 

13.24 

.46 

5.55 

455.8 

15.00 

5.87 

1.07 

60.8 

* 

42 

12.48 

.41 

5.5 

441.7 

14,62 

5.95 

1.08 

58.9 

12 

55 

16.18 

.82 

5.61 

321 

17.46 

4.45 

1.04 

53.5 


50 

14.71 

.70 

5.49 

303.3 

16.12 

4.54 

1.05 

50.6 


45 

13.24 

.58 

5.37 

285.7 

14.89 

4.65 

1.06 

47.6 

* 

40 

11.84 

.46 

5.25 

268.9 

13.81 

4.77 

1.08 

44.8 


35 

10.29 

.44 

5.09 

228.3 

10.07 

4.71 

.99 

38 

* 

31.5 

9.26 

.35 

5 

215.8 

9.50 

4.83 

1.01 

36 

10 

40 

11.76 

.75 

5.10 

158.7 

9.50 

3.67 

.90 

31.7 


35 

10.29 

.60 

4.95 

146.4 

8.52 

3.77 

.91 

29.3 


30 

8.82 

.46 

4.8 

134.2 

7.65 

3.9 

.93 

26.8 

* 

25 

7.37 

.31 

4.66 

122.1 

6.89 

4.07 

.97 

24.4 

9 

35 

10.29 

.73 

4.77 

111.8 

7.31 

3.29 

.84 

24.8 


30 

8.82 

.57 

4.61 

101.9 

6.42 

3.4 

.85 

22.6 


25 

7.35 

.41 

4.45 

91.9 

5.65 

3.54 

.88 

20.4 

* 

21 

6.31 

.29 

4.33 

84.9 

5.16 

3.67 

.90 

18.9 

8 

25.5 

7.50 

.54 

4.27 

68.4 

4.75 

3.02 

.80 

17.1 


23 

6.76 

.45 

4.18 

64.5 

4.39 

3.09 

.81 

16.1 


20.5 

6.03 

.36 

4.09 

60.6 

4.07 

3.17 

.82 

15.1 

* 

18 

5.33 

.27 

4 

56.9 

3.78 

3.27 

.84 

14.2 

7 

20 

5.8? 

.46 

3.87 

42.2 

3.24 

2.6? 

.74 

12.1 


17.5 

5.15 

.35 

3.7C 

39.2 

2.94 

2.7f 

.76 

11.2 

* 

15 

4.45 

.25 

3.66 

36.2 

2.67 

2.8< 

.78 

10.4 

6 

17* 

5.07 

.48 

3.5? 

26.2 

2.36 

2.27 

r .68 

8.7 


14* 

4.34 

.35 

3.4. r 

24 

2.09 

2.3.' 

) .69 

8 

* 

12? 

3.61 

.23 

3.33 

21.3 

1.85 

2.4( 

i .72 

7.3 

5 

14* 

4.3' 

.50 

3.2£ 

15.2 

1.7 

1.8' 

7 .63 

6.1 


12* 

3.6( 

) .36 

3. If 

13. < 

> 1.45 

1.9' 

1 .63 

5.4 

* 

9* 

2.8’ 

7 .21 

3 

12.] 

1.23 

2.0' 

3 .65 

4.8 


C. 


2115800 
2052900 
1990300 
1927600 
1855900 
1766100 
1713900 
1661600 
1609300 
1564300 
1353500 
1301200 
1247600 
1091900 
1044800 
997700 
943000 
1280700 
1241500 
1202300 
1163000 
1131300 
983000 
943800 
904600 
866100 
726800 
687500 
648200 
628300 
570600 
539200 
507900 
478100 
405800 
383700 
338500 
312400 
286300 
260500 
265000 
241500 
217900 
201300 
182500 
172000 
161600 
151700 
128600 
119400 
110400 
93100 
85300 
77500 
64600 
58100 
51600 
































































CARNEGIE ROLLED STRUCTURAL STEEL. 


33 


Carnegie Steel I Beams.— Continued. 


h. 

w. 

a. 

t. 

b. 

/. 


r. 

r'. 

s. 

C. 

4 in. 

10.5 

3.09 

.41 

2.88 

7.1 

1.01 

1.52 

.57 

3.6 

38100 


9.5 

2.79 

.34 

2.8 

6.7 

0.93 

1.55 

.58 

3.4 

36000 


8.5 

2.5 

.26 

2.73 

6.4 

.85 

1.59 

.58 

3.2 

33900 

* 

7.5 

2.21 

.19 

2.66 

6 

.77 

1.64 

.59 

3 

31800 

3 

7.5 

2.21 

.36 

2.52 

2.9 

.60 

1.15 

.52 

1.9 

20700 


6.5 

1.91 

.26 

2.42 

2.7 

.53 

1.19 

.52 

1.8 

19100 

* 

5.5 

1.63 

.17 

2.33 

[2.5 

.46 

1.23 

.53 

1.7 

17600 


Carnegie Steel Channels. 

(Sizes]with * prefixed are standard, others are special.) 


h. 

10. 

a. 

t. 

b. 

7. 


r. 

r'. 

S. 

C. 

X. 

15 m. 

55 

16.18 

0.82 

3.82 

430.2 

12.19 

5.16 

0.868 

57.4 

611900 

0.823 

50 

14.71 

.72 

3.72 

402.7 

11.22 

5.23 

.873 

53.7 

572700 

.803 


45 

13.24 

.62 

3.62 

375.1 

10.29 

5.32 

.882 

50 

533500 

.788 


40 

11.76 

.52 

3.52 

347.5 

9.39 

5.43 

.893 

46.3 

494200 

.783 


35 

10.29 

.43 

3.43 

320 

8.48 

5.58 

.908 

42.7 

455000 

.789 

* 

33 

9.9 

.40 

3.40 

312.6 

8.23 

5.62 

.912 

41.7 

444500 

.794 

12 

40 

11.76 

.76 

3.42 

197 

6.63 

4.09 

.751 

32.8 

350200 

.722 

35 

10.29 

.64 

3.3 

179.3 

5.9 

4.17 

.757 

29.9 

318800 

.694 


30 

8.82 

.51 

3.17 

161.7 

5.21 

4.28 

.768 

26.9 

287400 

.677 


25 

7.35 

.39 

3.05 

144 

4.53 

4.43 

.785 

24 

256100 

.678 

* 

20.5 

6.03 

.28 

2.94 

128.1 

3.91 

4.61 

.805 

21.4 

227800 

.704 

10 

35 

10,29 

.82 

3.18 

115.5 

4.66 

3.35 

.672 

23.1 

246400 

.695 

30 

8.82 

.68 

3.04 

103.2 

3.90 

3.42 

.672 

20.6 

220300 

.651 


25 

7.35 

.53 

2.89 

91 

3.40 

3.52 

.680 

18.2 

194100 

.62 


20 

5.88 

.38 

2.74 

78.7 

2.85 

3.66 

. 696 

15.7 

168000 

. 609 

* 

15 

4.46 

.24 

2.6 

66.9 

2.30 

3.87 

.718 

13.4 

142700 

.639 

9 

25 

7.35 

.62 

2.82 

70.7 

2.98 

3.10 

. 637 

15.7 

167600 

.615 


20 

5.88 

.45 

2.65 

00 8 

2.45 

3.21 

. 646 

13.5 

144100 

.585 


15 

4.41 

.29 

2.49 

50.9 

1.95 

3.40 

. 665 

11.3 

120500 

.59 

* 

13} 

3.89 

.23 

2.43 

47.3 

1.77 

3.49 

.674 

10 5 

112200 

.607 

8 

21} 

6.25 

.58 

2.62 

47.8 

2.25 

2.77 

.6 

11.9 

127400 

.587 

18} 

5.51 

.49 

2.53 

43.8 

2.01 

2.82 

.603 

11 

116900 

.567 


16} 

4.78 

.40 

2.44 

39.9 

1.78 

2.89 

.610 

10 

106400 

.556 


13} 

4.04 

.31 

2.35 

36 

1.55 

2.98 

.619 

9 

96000 

.557 

* 

11} 

3.35 

.22 

2.26 

32.3 

1.33 

3.11 

.63 

8.1 

86100 

.576 

7 

19} 

5.81 

.63 

2.51 

33.2 

1.85 

2.39 

.565 

9.5 

101100 

.583 


17} 

14} 

5.07 

.53 

2.41 

30.2 

1.62 

2.44 

.564 

8.6 

92000 

.555 


4.34 

.42 

2.3 

27.2 

1.40 

2.50 

. 568 

7.8 

82800 

.535 


12} 

3.60 

.32 

2.2 

24.2 

1.19 

2.59 

.575 

6.9 

73700 

.528 

* 

9} 

15.5 

13 

2.85 

.21 

2.09 

21.1 

.98 

2.72 

.586 

6 

66800 

.546 

6 

4.56 
3 82 

. 56 
.44 

2.28 

2.16 

19.5 

17.3 

1.28 

1.07 

2.07 

2.13 

. 529 
.529 

6.5 

5.8 

69500 

61600 

. 546 
.517 


10 5 

3.09 

.32 

2.04 

15.1 

.88 

2.21 

. 534 

5 

53800 

. 503 

* 

s 

2.38 

.20 

1.92 

13 

.70 

2.34 

.542 

4.3 

46200 

.517 

5 

11 5 

3.38 

.48 

2.04 

10.4 

.82 

1.75 

.493 

4.2 

44400 

. 508 


9 

2 65 

.33 

1.89 

8.9 

.64 

1 .83 

.493 

3.5 

37900 

.481 

* 

6 5 

1 95 

.19 

1.75 

7.4 

.48 

1.95 

.498 

3 

31600 

.489 

4 

7} 

6} 

5} 

6 

2 13 

.33 

1.73 

4.6 

.44 

1.46 

.455 

2.3 

24400 

.403 


1 84 

.25 

1.65 

4.2 

.38 

1.51 

.454 

2.1 

22300 

. ^58 

* 

1 55 

.18 

1.58 

3.8 

.32 

1.56 

.453 

1.9 

20200 

.464 


1 76 

.36 

1.6 

2.1 

.31 

1.08 

.421 

1.4 

14700 

.450 


5 

1 47 

.26 

1.5 

1.8 

.25 

1.12 

.415 

1.2 

13100 

. 4 4.8 

* 

4 

1.19 

.17 

1.41 

1.6 

.20 

1.17 

.409 

1.1 

11600 

.443 






































































34 


STRENGTH OF MATERIALS 


Carnegie T Shapes (Selected). 


Flange 

XStem, 

ins. 

w. 

a. 

X\. 

L 

S. 

r. 

r. 

S'. 

r’. 

C. 

4X5 

15.7 

4.56 

1.56 

10.7 

3.10 

1.54 

2.8 

1.41 

0.79 

24800 

4X5 

12.3 

3.54 

1.51 

8.5 

2.43 

1.56 

2. 1 

1.06 

.78 

19410 

4 X4£ 

14.8 

4.29 

1.37 

8 

2.55 

1.37 

2.8 

1.41 

.81 

20400 

4X4 

13.9 

4.02 

1.18 

5.7 

2.02 

1.2 

2.8 

1.4 

.84 

16170 

3X4 

10.6 

3.12 

1.32 

4.8 

1.78 

1.25 

1.09 

.72 

.60 

14270 

3X4 

9.3 

2.73 

1.29 

4.3 

1.57 

1.26 

.93 

.62 

.59 

12540 

3 X 

9.8 

2.88 

1.11 

3.3 

1.37 

1.08 

1.31 

.88 

.68 

10990 

3 X3£ 

i8. 6 

2.49 

1.09 

2.9 

1.21 

1.09 

.93 

.62 

.61 

9680 

3X3 

9 

2.67 

.92 

2. 1 

1.01 

.9 

1.08 

.72 

.64 

8110 

2^ X 3 

6.2 

1.8 

.92 

1.6 

.76 

.94 

.44 

.35 

.51 

6110 

24-X2i 

5.9 

1.71 

.83 

1.2 

.6 

.83 

.44 

. 35 

.51 

4830 

X 

5.6 

1.62 

.74 

.87 

.5 

.74 

.44 

.35 

.52 

4000 

2} X 2$ 

5 

1.44 

.69 

.66 

.42 

.68 

.33 

.30 

.48 

3360 

2jX2i 

4.2 

1.2 

.66 

.51 

.32 

.67 

.25 

.22 

.47 

2600 

2 X 2 

3.7 

1.08 

.59 

.36 

.25 

.6 

. 18 

. 18 

.42 

2000 

lfXlf- 

3.2 

.9 

.54 

.23 

. 19 

.51 

.12 

. 14 

.37 

1540 

1£X 1 £ 

2.6 

.75 

.42 

. 15 

.14 

.49 

.08 

. 10 

.34 

1150 

14x1 + 

2 

.54 

.44 

.11 

. 11 

.45 

.06 

.07 

.31 

860 

HXH 

2.1 

.60 

.40 

.08 

.10 

.36 

.05 

.07 

.27 

760 

1X1 

1.23 

.36 

.32 

.03 

.05 

.29 

.02 

.04 

.21 

370 

lxl 

0.87 

.26 

.29 

.02 

.03 

.29 

.01 

.02 

.21 

270 


Carnegie Steel Angles with Equal Legs. 

Max. and Min. Wts. Special Sizes marked *. „ 


Size. 

t. 

w. 

a. 

x 2 . 

8X8 

n 

56.9 

16.73 

2.41 

8X8 

+ 

26.4 

7.75 

2.19 

6X6 

i 

37.4 

11 

1.86 

6X6 

i 

14.9 

4.36 

1.64 

*5 X 5 

i 

30.6 

9 

1.61 

*5X5 

t 

12.3 

3.61 

1.39 

4X4 

JL3 

1 6 

19.9 

5.84 

1.29 

4X4 


8.2 

2.4 

1.12 

3£X3£ 

H 

17.1 

5.03 

1.17 

3£X3£ 

A 

7.2 

2.09 

.99 

3X3 

1- 

11.5 

3.36 

.98 

3X3 

i 

4.9 

1.44 

.84 

*2fX2f 

i 

8.5 

2.5 

.87 

*2iX2f 

i 

4.5 

1.31 

.78 

2£X2£ 

i 

7.7 

2.25 

.81 

2£X2+ 

A 

3. 1 

.9 

.69 

*21 X 2£ 

+ 

6.8 

2 

.74 

*2iX2i 

A 

2.8 

.81 

.63 

2X2 

7 

3 6 

5.3 

1.56 

.66 

2X2 

3 

3 <> 

2.5 

.72 

.57 

Hxh 

7 

1 6 

4.6 

1.3 

.59 

l|Xlf 

3 

1 6 

2.2 

.62 

.51 

Hx i + 

1 

3.4 

.99 

.51 

HXH 

£ 

1.3 

.36 

.42 

hxh 

5 

1 6 

2.4 

.69 

.42 

HX 1} 

£ 

1.1 

.3 

.35 

lxl 


1.5 

.44 

.34 

1X1 

£ 

.8 

.24 

.3 

*£X£ 

TS 

1.0 

.29 

.29 

*£X£ 

£ 

.7 

.21 

.26 

ixi 

A 

.9 

.25 

.26 

ixt 

£ 

.6 

.17 

.23 


L 

S. 

r. 

r". 

97.97 

17.53 

2.42 

1.55 

48.63 

8.37 

2.5 

1.58 

35.46 

8.57 

1.8 

1.16 

15.39 

3 53 

1.88 

1.19 

19.64 

5.8 

1.48 

0.96 

8.74 

2.42 

1.56 

.99 

8.14 

3.01 

1.18 

.77 

3.71 

1.29 

1.24 

.79 

5.25 

2.25 

1.02 

.67 

2.45 

.98 

1.08 

.69 

2.62 

1.3 

.88 

.57 

1.24 

.58 

.93 

.59 

1.67 

.89 

.82 

.52 

.93 

.48 

.85 

.55 

1.23 

.73 

.74 

.47 

.55 

.30 

.78 

.49 

.87 

.58 

.66 

.43 

.39 

.24 

.70 

.44 

.54 

.40 

.59 

.39 

.28 

.19 

.62 

.40 

.35 

.30 

.51 

.33 

.18 

.14 

.54 

.35 

. 19 

.19 

.44 

.29 

.08 

.07 

.46 

.30 

.09 

.109 

.36 

.23 

.044 

.049 

.38 

.25 

.037 

.056 

.29 

. 19 

.022 

.031 

.31 

.20 

.019 

.033 

.26 

.18 

.014 

.023 

.26 

.19 

.012 

.024 

.22 

. 16 

.009 

.017 

.23 

. 17 









































































CARNEGIE ROLLED STRUCTURAL STEEL 


35 


Carnegie Steel Angles with Unequal Legs. 

Max. and Min. Wts. Special Sizes marked *. 


Size. 

t. 

w. 

a. 

7. 

I'. 

S. 

S'.. 

r. 

r'. 

r" 

t* toipi^,*^ WMWCO ^ ^ 4-0icn0i0i0i0iai005 0s~j-^00 

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 

n 

1 

4 

1 

i 

1 

i 

l 

i 

l 

4 

i3 

1 6 

5 

T6 

1 3 

rs 

_5_ 

16 

JL1 

16 

5 

16 

13. 

1 6 

4 

1 3 

16 

1 6 

1 1 

1 6 

i 

4 

i 

4 

i 

i 

i 

\ 

4 

* 

3 

1 6 

i 

3 

1 G 

i 

i 

20.5 

32.3 

15 

30.6 

12.3 

28.9 

11.7 1 
24.2 
11 

22.7 

8.7 

19.9 
8.2 

18.5 

7.7 

18.5 
7.7 

17.1 

7.2 

15.8 
6.6 

12.5 

4.9 

9 

4.3 

9.5 

4.5 

7.7 

4.1 

6.8 
2.8 

5.6 

2.3 

2.7 

2.1 

1.9 

1 

6.02 

9.5 

4.4 

9 

3.61 

8.5 

3.42 
7.11 
3.23 
6.67 
2.56 
5.84 
2.4 

5.43 
2.25 

5.43 

2.25 
5.03 
2.09 

4.62 
1.93 
3.65 

1.44 
2.64 

1.25 
2.78 
1.31 

2.25 
1.19 

2 

.81 

1.63 
.67 
.78 
.60 
.53 
.28 

4.92 

7.53 

3.95 

10.75 

4.9 

7.21 

3.34 

9.23 

4.67 

6.21 

2.72 

3.71 
1.75 
3.6 

1.73 
5.49 
2.59 
3.47 
1.65 
3.33 
1.58 

1.72 
.78 
.75 
.4 

1.42 

.74 

.67 

.39 

.64 

.29 

.26 

.12 

.12 

.09 

.04 

.02 

39.96 

45.37 

22.56 

30.75 

13.47 

29.24 

12.86 

16.42 

8. 14 
15.67 
6.6 
13.98 
6.26 
10.33 
4.69 
7.77 
3.56 
7.34 
3.38 
4.98 
2.33 

4.13 
1.80 
2.64 
1.36 
2.28 
1.17 
1.92 
1.09 

1.14 
.51 
.75 
.34 
.37 
.24 
.09 
.05 

1.79 
2.96 
1.47 

3.79 
1.6 
2.9 
1.23 
3.31 
1.57 
2.52 
1.02 
1.74 

.75 

1.71 

.76 

2.30 

1.01 

1.68 

.74 

1.65 

.72 

.99 

.41 

.53 

.26 

.82 

.40 

.47 

.25 

.46 

.20 

.26 

.11 

.12 

.09 

.05 

.03 

7.99 
10.58 

5.01 

8.02 

3.32 

7.83 

3.25 

4.99 
2.34 

4.88 
1.94 
4.45 

1.89 
3.62 
1.54 
2.92 

1.26 
2.87 
1.23 
2.20 

.96 

1.85 

.75 

1.30 

.63 

1.15 

.56 

1.00 

.54 

.70 

.29 

.54 

.23 

.23 

.18 

.09 

.06 

0.9 
.89 
. 95 
1.09 
1.17 
.92 
.99 
1.14 
1.2 
.96 
1.03 
.80 
.85 
.81 
.88 
1.01 
1.07 
.83 
.89 
.85 
.90 
.67 
.74 
.53 
.57 
.72 
.75 
.55 
.57 
.56 
.60 
.40 
.43 
.39 
.40 
.27 
.29 

2.58 

2.19 
2.26 
1.85 

1.93 
1.85 

1.94 

1.52 

1.59 

1.53 
1.61 
1.55 
1.61 
1.38 
1.44 

1.19 
1.26 
1.21 
1.27 
1.04 
1.1 
1.06 
1.12 

1 

1.04 

.91 

.95 

.92 

.95 

.75 

.79 

.68 

.72 

.63 

.63 

.41 

.44 

0.74 

.88 

.89 

.85 

.88 

.74 

.77 

.84 

.86 

.75 

.76 

.64 

.66 

.64 

.66 

72 

.73 

.64 

.65 

.62 

.63 

.53 

.54 

.44 

.45 

.52 

.53 

.43 

.43 

.42 

.43 

.39 

.40 

.30 

.31 

.22 

.22 


Carnegie Steel Z Bars. 


Dimensions. 

1X3* X6 
T6 X 3 r 6 X 6 rV 
*X3* XG£ 
z\.X3h X6 
|X31®6 X 6 A 
i X 3f X6i 
|X3i X 6 
HX34X6A> 
iX3| X6i 
pt X 31 X 5 
1X34X5,J«r 
-4X3f X5i 


w. 

a. 

I. 

V 


S. 

S 


r. 

r 


r" 


6 

4 

59 

25. 

32 

9. 

11 

8. 

44 

2 

75 

2 

35 

1 

41 

0.83 

IS 

3 

5 

39 

29 

8 

10 

95 

9 

83 

3 

27 

2 

35 

1 

43 

. 84 

21 


G 

19 

34 

36 

12 

87 

11 

22 

3 

81 

<> 

36 

1 

44 

. 84 

22 

7 

6 

68 

34 

64)12 

59 

11 

52 

3 

91 

2 

28 

1 

37 


25 

4 

7 

46 

38 

86 14 

42 

12 

82 

4 

43 

2 

28 

1 

39 

. 82 

28 


8 

25 

43 

18 

16 

34 

14 

1 

4 

98 

2 

29 

1 

41 

.84 

29 

3 

8 

63 

42 

12 

15 

44 

14 

04 

4 

94 

2 

21 

1 

34 

.81 

31 

9 

9 

4 

46 

13 

17 

27 

15 

22 

5 

47 

2 

22 

1 

36 

. 82 

34 

6 

10 

17 

50 

22 

19 

18 

16 

4 

6 

02 

2 

.22 

1 

.37 

.83 

11 

6 

3 

4 

13 

36 

6 

18 

5 

34 

2 


1 

98 

1 

.35 

■ 75 

13 

q 

4 

1 

16 

18 

7 

65 

6 

39 

2 

45 

1 

.99 

1 

.37 

.76] 

16 

.4 

4 

.81 


.07 

9 

2 

7 

.44 

2 

.92 

1 

.99 

1 

.38 

• 7? ) 


C. 

90000 

104800 

119700 

123200 

130700 

150400 

149800 

162300 

174900 

57000 

08200 

79400 














































































36 


STRENGTH OF MATERIALS. 


Carnegie Steel Z Bars.— Continued. 


Dimensions. 

w. 

a. 

1 . 

I'. 

S. 

S'. 

r. 

r'. 

r". 

C. 

£X3£ X5 

17.9 

5.25 

19.19 

9.05 

7.68 

3.02 

1.91 

1.31 

.74 

81900 

AX3AX5A 

20.2 

5.94 

21.83 

10.51 

8.62 

3.47 

1.91 

1.33 

.75 

91900 

|X3| X5£ 

22.6 

6.64 

24.53 

12.06 

9.57 

3.94 

1.92 

1.35 

.76 

102100 

UX3i X5 

23.7 

6.96 

23.68 

11.37 

9.47 

3.91 

1.84 

1.28 

.73 

101000 

f X 3 A X 5A 

26 

7.64 

26.16 

12.83 

10.34 

4.37 

1.85 

1.30 

. 75 

110300 

HX3I X5£ 

28.3 

8.33 

28.70 

14.36 

11.2 

4.84 

1.86 

1.31 

.76 

119500 

i X 3 A X 4 

8.2 

2.41 

6.28 

4.23 

3. 14 

1.44 

1.62 

1.33 

.67 

33500 

A X 3£ X 4 A 

10.3 

3.03 

7.94 

5.46 

3.91 

1.84 

1.62 

1.34 

.68 

41700 

IX3AX4* 

12.4 

3.66 

9.63 

6.77 

4.67 

2.26 

1.62 

1.36 

.69 

49800 

A X 3 A X 4 
£ X 3£ X4A 

13.8 

4.05 

9.66 

6.73 

4.83 

2.37 

1.55 

1.29 

.66 

51500 

15.8 

4.66 

11. 18 

7.96 

5.5 

2.77 

1.55 

1.31 

.67 

58700 

A X 3 A X 4£ 

17.9 

5.27 

12.74 

9.26 

6. 18 

3.19 

1.55 

1.33 

.69 

65900 

£ X3A X4 

18.9 

5.55 

12.11 

8.73 

6.05 

3.18 

1.48 

1.25 

.66 

64500 

rk X 3£ X4A 

20.9 

6. 14 

13.52 

9.95 

6.65 

3.58 

1.48 

1.27 

.67 

70900 

|X3AX4£ 

23 

6.75 

14.97 

11.24 

7.26 

4 

1.49 

1.29 

.69 

77400 

£X2f£X3 

6.7 

1.97 

2.87 

2.81 

1.92 

1 . 1 

1.21 

1.19 

.55 

20500 

A X 2£ X 3 A 

8.4 

2.48 

3.64 

3.64 

2.38 

1.4 

1.21 

1.21 

.56 

25400 

| X 2 ! ,V X 3 

9.7 

2.86 

3.85 

3.92 

2.57 

1.57 

1.16 

1. 17 

.55 

27400 

AX2f X 3A 

11.4 

3 . 36 

4.57 

4.75 

2.98 

1.88 

1.17 

1.19 

.56 

31800 

£ X 21£ X 3 

12.5 

3.69 

4.59 

4.85 

3.06 

1.99 

1.12 

1. 15 

.55 

32600 

AX2£ X3A 

14.2 

4.18 

5.26 

5.70 

3.43 

2.31 

1.12 

1.17 

.56 

36600 


REINFORCED CONCRETE CONSTRUCTION. 

A reinforced concrete construction is one where concrete and steel are 
used jointly, being proportioned to carry the strains of compression and 
tension respectively. Such constructions have all the advantages of a 
purely masonry construction along with the elasticity of one of steel. They 
are permanent, proof against fire, rust, rot, acid, and gas and do not 
require attention, repair, or painting. Moreover, thh' strength of concrete 
increases with age, and a safety factor of 4 at the time of completion of 
structure may easily amount to 6 or 7 after the lapse of a year or so. 

Advantages. Crushed stone, sand, and cement are procurable on 
short notice, while structural steel is often subject to long delays in deliv¬ 
ery. Concrete, may be molded into any desired form, and masonry simu¬ 
lated. Deflection under safe load is practically nil. It being essential that 
a beam fail by the parting of the steel, after its elastic limit has been 
exceeded the stretch is such that a reinforced concrete beam should deflect 
several feet before failure. 

Design. The concrete should be reinforced in both vertical and hori¬ 
zontal planes, the vertical reinforcement being inclined at an angle of 45° 
to the horizontal and approximating thereby the line of principal tensile 
stress. The shear members should be rigidly connected to the horizontal 
reinforcing steel. Steel should be distributed proportionally to the stress 
existing at any point. 

The concrete should be composed of the best grafle of Portland cement, 
sharp, clean sand and broken stone or gravel (to pass a 1-in. ring) in the 
proportions 1 • 2.5 : 5 for floor slabs and 12 4 for beams. Steel bars 

should be at least 0.75 in. from bottom of beam. The concrete should 
be thoroughly rammed into place and the centering left in position for at 
least IS days, and, if freezing has occurred, for such additional time as 
may be required for every indication of frost to vanish and for the con¬ 
crete to become thoroughly set. 

Methods of Calculation. Beams. For span take (list, c to c of 
bearings (for slabs, the clear span + slab thickness; if continuous over 
more than one span, take dist. c. to c. of beams). 

Maximum Bending Moments: Beam or slab supported at ends wl 2 -*- 8 
(in.-lbs.); continuous or fixed beam, not less than wl 2 +12 

Coefficients of Elasticity: Es (steel) =30,000,000. E c (concrete) for a 






















REINFORCED CONCRETE CONSTRUCTION. 


37 


mixture not weaker than 1:2:4, may be taken as equal to 2,000,000 

lis hr— lo. 

That part of the concrete above the neutral axis is assumed to carry the 
compression, the stress varying uniformly from 0 at the neutral axis to a 
maximum at the compressed edge. 

The steel reinforcement is assumed to carry all the tension, the stress 
being uniform over its cross-section. 

W °rking Stresses:—If the concrete is of a quality such that its crushing 
strength after 28 days is 2,400-3,000 lbs. per sq. in., and the steel has a 
tenacity >or— 60,000 lbs. per sq. in., the following stresses may be allowed: 


Concrete, in compression in beams subjected to bending. 600 lbs. per sq. in. 

Concrete in columns under simple compression. 500 “ “ ‘‘ “ 

Concrete in shear in beams. 60 “ “ “ “ 

Adhesion of concrete to steel.. . 100 “ “ “ “ 

Steel in tension.15,000 to 17,000 “ “ “ “ 


For other concrete, allowable stress= I X crushing strength (JX crushing 
strength for columns). For steel of a different strength, allowable stress 
= iXstress at yield-point. 


Let b— width of beam in inches. 

d= depth of beam (top to center of steel bars) in inches. 
bi= width of upper flange of T beam (slab) in inches. 
di= thickness of upper flange of T beam (slab) in inches. 

(&i should not be greater than §Z or f dist. c. to c. of floor-beams. 

di is generally from — to —. ) 


A —bd— area of cross-section. 

m— E s E c . 

M= bending moment at section considered in inch-pounds. 
t— tensile stress in steel in lbs. per square inch. 
c= compressive stress in concrete in lbs. per square inch. 
z= distance of resultant thrust in concrete from compressed edge of 
beam in inches. 

kd— distance from compressed edge to neutral axis, in inches. 

A c = kbd= area of concrete in compression in square inches. 

At= area of steel in tension in square inches. 

V— At-r- bd= ratio of steel to concrete = percentage of reinforcement. 
Z= span in inches. 

w= load per inch run of span (weight of reinforced concrete may be 
taken as 150 lbs. per cu. ft.). 


It can be shown that 


k= v p 2 m 2 + 2 pm — pm. 


and also that 




M 


pt{ 1 — hk) 

2 M 


kc(l-iky 

For T beams, where dy~>kd, 

A—b\d\ + b(d — di)- 

and 


M 


pdt(l-hk) 


M 2 = 


2 M 


When di < kd. 


and 

where 


A = 
bid t = 


kc (1 — ik) 
M 


pt(d — z ) 

2Mkd 


c(2kd — d\) (d — z)' 


_d\ s/ 3kd—2di 
2 kd-d x ' 


( 1 ) 

/ 

( 2 ) 

(3) 

,(4) 

(5) 

\ 

( 6 ) 

(7) 

( 8 ) 

















38 


STRENGTH OF MATERIALS. 


Stirrups or rigidly attached web members or inclined bars should be 
provided at and near the ends of the beams where the average shearing 
stress on a vertical section exceeds 60 lbs. per sq. in. of the beam section. 

The adhesion required in the case of a uniformly loaded beam, supported 
at the ends, with horizontal steel bars not turned up at the ends, is found 
as follows: 

The difference of tension in 1-ft. length of bars at end of span = tangential 
force between the steel and concrete in that distance. At the end, M=0, 
and at 1 ft. from end M—§w{l —12) in.-lbs. .'. increment of tension be¬ 
tween the end and 1 ft. from the end is 6w(l— 12) -5-d(l — %k) lbs. 

If n— total perimeter of reinforcing bars, the adhesion stress in lbs. 
per sq. in.= w(l— 12) -s- 2nd(l — %k). 

Example:—Design a. beam, freely supported at the ends, of 12 ft. span 
to carry 960 lbs. per lineal foot, using 1% of reinforcement (p=0.01). 

Taking m= 15, £=0.418 [from (1)]. 

Assume t— 16,000 lbs. per sq. in., w— 960-t- 12= 80 lbs. per inch run, 
Z= 12X12= 144 ins., M= wl 2 + 8= 207,360 in.-lbs. 

Substituting these values in (2), 

bd 2 = 207,360 ^[0.01 X 16,000(1-0.418)]= 2,227. 

For a trial value take 6= 12 ins. Then, d 2 = 185, and d= 13.5 in. Add¬ 
ing 1£ ins. to bottom of beam to protect the steel bars, gives a total depth 
of 15 ins. 

A beam 12X15 ins. will weigh 15.6 lbs. per lineal inch, consequently 
w should be taken=80+16 say, and another calculation made, which will 
include the weight of the beam, approximately. 

(The foregoing simple methods are those embodied in the Report of the 
Reinforced Concrete Committee, formed under the auspices of the Royal 
Institute of British Architects, and are undoubtedly as reliable as any 
that can be cited.) 

Columns. —Let P= total weight to be supported by column in lbs.; and 
A s = sectional area of steel reinforcement. Then, using the notation 
under “Beams”: 

For light longitudinal reinforcement (less than 1%), P—c(A + mA s ). (1) • 
For heavy “ “ (1% and over), P= t[A + (m — 1)A S ]. (2) 

Example:—Design a column to sustain 40,000 lbs., using 1% reinforce¬ 
ment. c=500; ?n= 15. Substituting in (2) (A S =0)01A), 

40,000= 500[A + (15 — 1)0.01.4.3 
= 500X1.14A=570A, 


and A = 70 sq. ins.= 8.4 ins. square or 9.5 ins. diarn. 

The longitudinal bars should be bound around by steel straps or rods 
to prevent their bending, and these straps should not be spaced apart 
more than 24 times the least lateral dimension of the longitudinal bars. 
^Spiral Hooped Columns:— 

P=0.6^1.178cd 2 + ~ - 54 ^ dd j, 


where d=diam. of prism and hooping, A s = sectional area of steel in the 
hoops or wire, and s— spacing of hoops or spirals—generally from ^ to 


Take c=400 and t— 15,000. 

These formulas hold where the length of the column is not greater 
than 18 times the diameter or least lateral dimension. Few cases arise 
in practice where such a length is exceeded. 

As the adhesion between the steel and concrete in the case of smooth 
bars is open to uncertainty, many bars have been devised which give 
a positive bond, through being twisted, corrugated, indented or otherwise 
deformed at close intervals along their length. 

Summary of Beam Tests. From about 200 reported tests, T. L. Con- 
dron (W. Soc. of Engs., 3-15-03) deduces the following formula. Ult. 
Bm (in inch-lbs.) = (nP+55)5d 2 , where n — 450 for highly elastic steel bars 
positively bonded to the concrete ( = 275 for plain bars of ordinary struc¬ 
tural steel); P=percentage of reinforcement = (100Xbar section)-t-bd; b 
and, d, in inches. ^ 



REINFORCED CONCRETE CONSTRUCTION. 


39 


For ordinary concrete (1 3 6) P may vary from 0.5 to 1.25, economy 
lying between 0.7 and 0.9. For extra strong concrete (1 2 4) P may be 
increased to 1,25» 


Stress Diagrams in Framed Structures. If three oblique forces 
maintain a body in a state of rest, their directions meet at one point and 
their proportional values may be shown by the respective sides of a tri¬ 
angle drawn parallel to the forces. . 

If a body remains at rest under the action of a number of forces m the 
same plane, their relative magnitude may be shown by a polygon whose 
sides, taken in order, are drawn parallel to the forces. 



General Case. Simple Roof Truss (Fig. 6). 

\ weight of ab(W) will be supported at each point, a and b- 
i “ “ ac(IF) “ “ .. “ a “ e. 


The weight, then, at a 


W+W' 

2 


The reaction at R which balances a = 
•• “ “ R' “ “ a = 


W+W' x 

2 ' r 

W+W' l-x 
2 * l * 


W W+W' 
Total reaction at R = — d- ^ - 


«' = 


IF . W + W' 


x_ 

* V 

l — x 


2 


l 

































40 


STRENGTH OP MATERIALS. 


Thp forces bein'* thus stated, letter each cell or enclosed space (in this 
eai but one, i.e rthe triangle A), and also each section of the external 
space as divided by the lines of the forces and the members of the truss, 

J 



M 

H 

L 

K 










































STRESS DIAGRAMS. 


41 


nut,—preferably right-handed). Set off in the force diagram FR — - and 

HC = R' = Draw AE parallel to the right member of 

truss, ac; then AC will be parallel to be and meet BC at point C (see I). 
Notice that arrows must follow each other around the diagram in one 
direction. II and III show direction of forces for points a and b. AF, 



AC, and AE in the force diagram are then the stresses in ^he numbers of 
the truss and are measurable by the scale assumed for W and IE . Hace 
nrrnws on the members of the truss as indicated by 1, II, and ill , tnen, 
pointing lunrdeaA other show that the member » m tension and 

ihT plication of 

thp it receding principles. Redundant members (those not stressed ex 
cepting w&lisJortion takes place) may be determined by mspecDon^and 
their number = the number of members m excess of [(twice the number ot 

ioints) — 3]. 




















42 


STRENGTH OF MATERIALS. 


Fig. 7 shows the stresses in a symmetrically loaded Warren truss, i.e., by 
the weight of its members. Fig. 8 shows the same truss under any concen¬ 
trated load W, which may be taken for a rolling load by determining the 
stresses caused at each joint by imposing this load, and designing each 
member for the maximum stress it may have to withstand Note from 
BC, CD (Fig. 8), as compared with same members in b ig. 7, that t he mem¬ 
bers are subject to either tensile or compressive stress and should be cal¬ 
culated for the greatest stress of each kind. p , . ™ 

In the rafters of the roof-truss (Fig. 10) the load on each ratter — H , 
and having three supports, is divided (as per table for Continuous Beams, 
81F 10W 

ante ) as follows: — at each end support and -pp on the middle support. 

The total horizontal wind pressure, P/f = 40 to GO lbs. per sq. ft. X width of 
bay between two rafters X& (see diagram)] is resolved into two compo- 

nentc,—one parallel, and one normal to the rafter. The latter, Pn = 

, , 3 Pn 5Pn , 3 Pn ,. , 

and is distributed at a, d, and c as -y^-, ~~g~* anf l “Jg - * respectively. 

If a be fixed and b loose, expansion is provided for, and the reaction 
R' is vertical. R, R', and Pn mutually balance and meet in the point x 
(found by producing Pn to intersect R')- By connecting R and x the 
direction of R is given and values of R and R' are obtained from the auxil¬ 
iary force diagram. If the wind blows from the right, Pn acts on be, and 
x will be above instead of below b. Each member should be designed to 
resist the maximum stresses in it caused by the weight of roof, rafters, 
snow, and also the wind pressure, from whichever side a maximum stress 
in the particular member is caused. 

Framed Structures of Three Dimensions must be solved by con¬ 
sidering each plane of action separately. For example, in a shear legs 
substitute for the two rigidly attached legs a single one in a plane with 
the third or jointed leg, determine the respective stresses, and then resolve 
the stress in the substituted leg into the stresses for the two legs it replaces. 


A 


1 







ENERGY AND THE TRANSMISSION 

OF POWER. 


Force and Mass. The unit of force in engineering is one pound avoir. 

, . , . , , weight, 

dupois. Mass, or the quantity of matter contained in a body, = 


0 

0 = 32.16954(1-0.00284 cos 21) (1 where 

r = 20,887,510(1+ 0.00164 cos 21) ,'in which Z = latitude in degrees, 

= height above sea-level in feet, and r = radius of the earth in feet. In 
calculations g is ordinarily taken as 32.16 in the U. S. , T , 

Velocity, or the rate of motion, is estimated in ieet per second, 11 uni¬ 
form. s = y. If uniformly varying from Vi at beginning, to v 2 at the end 
. V\ + Vo 

of the time t, s =— z t 

Acceleration (/) is the increase of velocity during each second, and, if 
uniform, is produced by any constant force, the force being measured by 
the increase of momentum it produces. Momentum, or the quantity ot 
motion in a body = mass X velocity =mv, and force producing acceleration 

= w f-L.g' f = V ——— (2). Combining (1) and (2), s = i’i^ + —(3). Ifvj = 0 
t 


( 1 ). 




(4) and f = ~f (5). 

L 


Substituting 

-vit—2" 


(starting from a position of rest), s = 

(5) in (4), Vo 2 = 2/s (6). For retarded motion (3) would read: 

Inmact of Inelastic Bodies. Two inelastic bodies after collision will 
move as one mass with a common velocity, and the momentum of their 
combined mass is equal to the sum of the momenta before impact. 

(m 1 +m 2 )v(final)=m 1 i ; 1 + m 2 i; 2 . v = accordin ^ as the bodie8 

move in the same or in opposite directions before collision. 

The Pendulum. A simple pendulum is a material point acted upon by 
the force of gravity and suspended from a fixed point by a line haying no 
weight. A compound pendulum is a body of sensible magnitude sus¬ 
pended from a fixed point by a line or r.xl whose weight must be considered. 
The center of oscillation is a point at which, if all the weight of a compound 
pendulum be considered to be there concentrated, the oscillations will 
have the same periodicity as a simple pendulum. The distance of the 
center of oscillation from the point of suspension = (radius of gyration)*- 
distance of center of gravity from point of’ suspension (a). An ordinary 
pendulum oscillates in equal times (isochromsm) when the angle of oseil- 

a Let Z=thstance in in. between point of suspension and center of oscilla¬ 
tion of a simple pendulum, t = time.in seconds for n oscillations, and n- 
number of single oscillations^one^side to the other) in time t. Then, for a 

simple pendulum, l= „ ^ = n 2 


43 








44 ENERGY AND THE TRANSMISSION OF POWER. 


4 CL T~ 

For a compound pendulum (rod of radius r): Z = -g-+^-; 

2 r * 2 

“ “ “ (ball of radius r): l = a + —. 

“ “ “ ball of weight IF (dist. a) and ball of IFi 

, . f . , a*W + ay*Wy 

vdist. a i), both on same side of point of suspension; 1= a -\y + a yWy ' 

Balls W(a ) and IFi(ai), point of suspension between: dist. of c. of g. of 

system, x— W+Wi . and Z + 

In the last two cases W is the larger weight, and the weight of connecting 
line or rod is neglected. The length of a simple pendulum which oscillates 
seconds at New York is 39.1017 in. 

Energy, or the capacity for performing work, is of two forms: Potential 
Energy, which is stored or latent, and Kinetic Energy, or the energy of 
motion. In any system, kinetic energy + potential energy = a constant. 
In any machine the energy put in = the useful work given out + the 
work lost by resistances. (Stored energy not considered.) Either kind of 
energy may be transformed into the other kind. 

Estimate of Energies. The Potential Energy of a weight w, at 
height H = wH ft.-lbs. If allowed to fall, the velocity on reaching the 

ground, r = v / 2/s, from (6). But f = g, and s = H, .". v = x/ 2gH and H = —. 

2 0 

Substituting (in tcH), Energy (now Kinetic) in ft.-lbs. = — , which is ap¬ 
plicable to all cases of moving bodies, it being strictly proper to assume 
that the velocity is caused by gravity. 

When a body rotates around an axis (e.g., rim of fly-wheel, of weight, w), 

( N \ WV^ 

n = — J and the Energy of Rotation in ft.-lbs. = = 

w(2nRN) 2 


= 0.0001704 wR z N 2 . 


wL 


ft.-lbs.; the Energy of a 


20 ( 60)2 

The Energy of a Compressed Spring 

Compressed Gas = mean effective total pressure X stroke. 

The Energy of One Heat Unit (1 B.T.U. = 1 lb. water raised 1° F. 
when near 39°) = 778 ft.-lbs. 


Energy of Power Hammers. Energy of falling hammer = 


wv z 

V 


En¬ 


ergy received by the hot iron = mean total pressure in lbs. p, X depth of 


impression H, in feet, and pH = 


wv* 


2 o' ‘ ‘ V ~ 2gH‘ 
pressure = 2 p. ' 

Energy of Recoil. Let wy and w 2 = weights of gun (wdth carriage) 
and projectile; vi and v 2 =velocity of recoil and projectile velocity at 

muzzle. Then, wyvy = w 2 v 2 and = The energy of a body in motion = 

W\ 

hence the energy of recoil = wy -r-2 g, and the energy of the 

2 g \ wy / 

projectile = w^ 2 2g. 

Power is the rate at w T hieh w’ork is performed, the unit being one horse¬ 
power, or 33,000 foot-pounds exerted during one minute. 

Elements of Machines. • A machine is an assemblage of parts w’hose 
relative motions are fully constrained, and its purpose is the transmission 
or the modification of power. Let P be the point where the power is 
applied and W the point where it is removed or utilized. Then, work 
put in at P = work taken out at W (neglecting resistances). As w r ork = 

W s 

force X distance, Ps = Wsi, or -p = —, where s and Siare the distances traveled 
by P and W. Further, 

velocity of P force IF , . . . , W 

— ,— - -Trir—c -n = Mechanical Advantage, vr. 

velocity of IF force P> P 


wv* 


The greatest total 











ELEMENTS OF MACHINES. 


45 


The Lever. By the principle of moments, Pr=Wr\ and the 

IV r 

Mechanical Advantage = 77 =—, r and r\ being the respective radii of 

P r\ 

P and IE from the fulcrum (for straight lever and parallel forces). 

Lever Safety-Valve. Let w, w\, and IE be the weights of lever, valve, 
and ball, respectively in lbs., r, r\, and R the distances from center of 
gravity of lever, valve center, and ball center to fulcrum, in in., d the 
valve diam., in in., and p the steam pressure per sq. in. of valve. Then, 


IE = 


(0.7854pd 2 — U’i)ri — wr 


R 

If the lever is bent or the forces are not parallel, the arms rj and R are 
then equal to the length of the perpendicular drawn from fulcrum to the 
line of direction of each force. 

, . . , .,,, . r wheel radius 

Wheel and Axle. Mechanical Ad vantage =-^ = radius "’ 

Train of Gearing. P is applied at radius of first wheel, transmitted 
by its toothed axle to circumference of second wheel which is toothed, 
by second axle circumference to third wheel circumference, etc. 

W T\ 7*2 7*3 

Mechanical Advantage, p == ^X-^ X^ 3 , etc. 

Block and Tackle. The pull P on the rope through the distance « 
will raise the weight IE through the distance 


* 1 = 


No. of plies of rope shortened by the pull' 


Mechanical 
IE 


Advantage = ^7 = 


No. of plies shortened 

1 


In any movable 


pulley, -p =-p ^ rising only one-half the height that P does. 

Differential Pulley. Two pulleys whose diameters are d and d\ rotate 
as one piece about a fixed axis. An endless chain passes around both 
pulleys and one of the depending loops of the chain passes around and 
supports a running block from which IE is hung. P is applied on the 
chain running directly to pulley of larger diam., d. 


Mechanical Advantage = p 


IE P’s dist. 


zd 


2d 


IE’s dist. zd — zd\ d — d\ 


Inclined Plane and Wedge. While P moves through base b, W is 

W b • 

raised through the height h, and Mech. Adv. = p =p. A cam is a revolving 

inclined plane. , , , 

The Screw is an inclined plane wrapped around a cylinder so that the 
height of the plane is parallel to the axis of cylinder. It is operated by 
a force applied at the end of a lever-arm (of length r) perpendicular to 
axis. Let p" = pitch of screw = height of inclined plane for one revolu- 

, , IE P’s dist. 2 nr 
tion of screw. Then, Mech. Adv. =p = WxTdIsL — ?E r ' 

Connecting-Rods are subject to alternate tension and compression 
and the diam. dj at mid-length is calculated by means of Gordon’s formula 
for columns (both ends hinged) where r 2 = d] 2 -n16, using a safety factor 
of 10 and values of a and b for steel. The diam. at small end ( d ) is designed 
to resist compression only, that, at large end (d 2 ) being obtained by con¬ 
tinuing the taper from small diam. to diam. at mid-length and thence to 
the large end, and is equal to 2 d x -d. Kent gives as the average of a 
large number of formulas considered by him: = 0.021 Xdiam. of 

cylinder X^p (steam). Barr gives as the average of twelve Am. builders: 
d] = 0.092Vcyl. diam. Xstroke (for low-speed engines ), and thickness, t 

(for rectangular sections, high-speed engines) = 0.057^ diam. cyl, X stroke 
breadth = 2. 7t. All dimensions in inches. 












46 ENERGY AND THE TRANSMISSION OF POWER. 


Connecting-Rod Ends. Strap-end: width = 0.8m, thickness = 0.22m 
(increased to 0.33m at mid-length and also at ends when slotted for gibs 
and cotter); depth of butt-end of rod = l.ld + Ain. d = diam. of crank-pin, 

m Crank-Arms (Wrought Iron). Hub diam. = 1.8d; hub length = 0.9rf; 
diam. of crank-pin eye = 2eh; length of eye = 1.4di; width of web = 0.75 X 
rliam. of adjacent hub or eye; thickness of web = 0.6Xlength of adjacent 
hub or eye (d== least diam. of shaft; ch = diam. of crank-pin). 

, A /total pressure on valve area 
Valve-Stems. Diam., d 3 = 'V -1^000- 

Eccentrics. Sheave diam. = (2.4 Xthrow) + (1.2 Xshaft diam.); breadth 
= c ?3 + 0.6 in.; thickness of strap = 0.4d 3 + 0.6 in. (d 3 = diam. of valve- 
stem.) 


SHAFTING. 


For strength against permanent deformation, d 


»/ 

= 3.33T 


H.P. 
N ' 


For 


stiffness to resist torsion (max. allowable twist<0.075° per foot in length), 


w = 4 7 i/ 54 L\ These values are for W.I.; for steel shafts d has but 84% 
N 

of the values given by formulas. In designing take the larger of the two 
values of d obtained from th e form ulas. 

Average Practice. ^ , where c (for cold-rolled shafting) 

for shafts carrying pulleys =75; for line shafting, hangers 8 ft. apart, = 55; 
for transmission only, =35. For turned iron shafting under similar con¬ 
ditions multiply value of c by 1.75. . . 

Length between bearings to limit def lection to 0.01 in. per foot of shaft¬ 
ing: for bare shafts, L (in feet) = 1^/720d 2 ; for shafts carrying pulleys, 
L = ^/l40d 2 . 

Fly-wheel Shafts. For shafts carrying fly-wheels, armatures or 
other heavy rotating masses, find the equivalent ( twisting moment of 
the combined torsion and bending in inch-lbs. and apply same in the two 
formulas at the beginning of this topic, remembering that 


Twisting moment = 


33,000.12 

2n 


ILP._™ nor H P - 
jy 63,0-o . 


(See p. 31.) 


Average Engine Practice. 


Crank-shaft diam., 


d = 6.8 to 7.3 X 


V 


H.P. 

N 


for low and high speed respectively (Barr). Also, d = 0.42 to 0.5Xpiston 
diam. (Stanwood). N for machine-shops = 120 to 180; for wood-working 
shops, 250 to 300; for cotton and woolen mills’, 300 to 400. 


JOURNALS. 

The allowable pressure p in lbs. per sq. in. on the projected area ( iXd) 
of journals is as follows: For very slow-speed journals, p = 3,000; for 
cross-head journals, p= 1,200 to 1,600; for crank-pin journals, low speed, 
p = 800 to 900; ditto, Am. practice, 1,000 to 1,200; for marine engine 
crank-pin journals, 400 to 500; railway journals, 300; crank-pin journals 
for small engines, 150 to 200; main bearings of engine, 150; marine slide- 
blocks, 100; cross-head surfaces, 35 to 40 lbs. per sq. in.; propeller thrust- 
bearings, 50 to 70; main shafting in cast-iron boxes, 15. 

Overhung Journals. On end of shaft. Constant pressure. When 

)V<150, d = 0.03v / P for W. I., and 0.027 ^P for steel; -^- = 1.5 to 2. When 

2V>150, d = 0.0244^7P-i-d for W. I. and O.OlOv^P-j-rf for steel. Also 

4- = 0 . 13 vW for W. I. and 0.17 ^N for steel. 
d 


















BALL AND ROLLER BEARINGS. 


47 


Journals under Alternating Pressures (e.g., crank-pin). When 

N < 150, d = 0.027^ / P for W. I. and 0.024^^ for steel; ~=1 for W. I. 

a 

and 1.3 for steel. When N> 150, d = 0.02734^-y~ for W. I. and 0.02\^~ 

a a 

for steel; -^- = 0.08^^ for W. I. and 0.1 ^/n for steel. Am. Engine Prac¬ 
tice: d (for crank-pin) = 0.22 to 0.27Xpiston diam.; 1 = 0.25 to 0.3Xpis- 
ton diam. (Stanwood). Cross-head pins: di = 0.8d; Z 1 = 1.4d 1 . 

Neck Journals, or those formed on the body of shaft need but two- 
thirds the diameter of overhung journals of the same length. For ball 
and socket shaft-hangers, Z = 4d; depth of shoulder on neck journal may 
be taken as 0.07d + i in. 

Pivots. For iV<150, p = 700, 350, or 1,422 lbs. per sq. in., and 
d ' = Vpx0.05, 0.07, or 0.035, for W.I., on bronze, C.I. on bronze, and 
W.I. or steel on lignum-vitse, respectively. For N>150, d = 0.004v / pzV 
and 0.035^^ for W.I. (or steel) on bronze and lignum-vitae, resp ectively. 

Collar Bearings. Outside diam. D = ]/ d 2 + Thick- 

47 Xno. of collars 

ness of collar = 0.4(D — d) = ^Xspace between collars. (d = shaft diam.). 

Shaft Couplings. For a cast-iron keyed sleeve-coupling, / = 2.G6d + 
2 in.; external diam. of sleeve = 1.66d +0.5 in. For a cast flange coupling, 
l of hub on each half =1.33d+l in.; hub diam. = 1.66d + 0.5 in.; flange 
diam. = 2.5d + 4 in.; flange thickness = 0.166d +0.42 in.; width of flange 

rim = 0.35d +0.86 in.; no. of bolts = 2 + 0.8d; diam. of bolts = ^ in. 

O 

For plates forged on abutting shaft ends, Z = 0.3d; outside diam. = 
1.6d + (2.25Xbolt diam.); no. of bolts = —. {d = shaft diam.) 

Brasses should have a thickness in the center (where wear is greatest) 

^0.16d-l- 0.25 in. 

BALL AND ROLLER BEARINGS. 

Roller Bearings. Let n = number of rollers; d = diam. of rollers in 
in. (for conical rollers take diam. at mid-length); 1 = length of rollers in 
in.; then, if the rollers are sufficiently hard and are so disposed that the 
load is equally distributed over l and n. Load in lbs. P = cnld, where c = 355 
for C. I. rollers on flat C. I. plates, and 850 for steel rollers on flat steel 
plates (Ing. Taschenbuch). 

Friction may be reduced 40 to 50% by the use of roller bearings. 
The Hyatt flexible rollers consist of flat strips of springy steel wound 
spirally into tubular form; they give at all times a contact along their 
entire length. It is claimed for them that they save 75% of the lubrica¬ 
tion (and 10 to 25% of the power) needed by ordinary bearings of equal 
capacity, and that they cannot become overheated. 

Ball Bearings. Diam. of enclosing circle = (d + c)F + d, where d = diam. 
of ball; c = clearance betw T een each pair of balls; F, a factor as follows: 


No. of balls. 14 15 16 17 18 19 

Factor F . 4.494 4.8097 5.1259 5.4423 5.7588 6.0756 

No. of balls. 20 21 22 23 24 

Factor F . 6.3925 6.7095 7.0266 7.3338 7.6613 


d + c 

or, generally, D = d-\ -where n = no. of balls. 

sin- 

n 

If 0.005n>—, take c = — —; otherwise, c = 0.005. All dimensions in 
4 n 

inches. 










48 ENERGY AND THE TRANSMISSION OF POWER 


Crushing Strength of Balls. 


Breaking Load in Lbs. 


d 


i 

i 

a 

+/ 


If 

1 


Ball on 

Between Flat 

Ball. 

Plates. 

1280 

1814 

4153 

6570 

9030 

12700 

16710 

22610 

28580 

30J00 

59030 

90650 


Auto Machy. 

Safe 

Co. 

Load. 

1238 

160 

515J 

640 

11600 

1450 

206JO 

2570 

32260 

4030 

S240J 

10300 


Tiie Auto Machinery Co.’s data answer to breaking load = 82,400d 2 
and are a fair average of the first two columns (results obtained by 4. J. 
Harris at Rose Polytechnic institute), the su laie of ball race being con¬ 
sidered as between a sphen.ai and a pia. e su face. 

. „ total load X 5 . , , 

Greatest load on a single ball = oi 111 an annular bearing 

where n ranges from 10 to 18 (Stribeck, Ing. Taschenbuch). Prof. C. H. 
Benjamin recommends a safety factor of 10, that in above table is 8. 

Radial Ball Bearing, with 4 point contact. -P( sa f e ) = (««) • 

If P> 3,000 lbs., P — 300 + 290?td. „ x 

Thrust Bearing, with 3 point contact. F( sa f e )(l,000 to 4 > 500 lbs.) — 

l,143(nd-2i); P( sa fe)( 4 - 500 to lbs.) = 2,125(«d-4); P (sa f e )(8,500 

to 17,000 lbs.) == 1,500 + 808nd. 


Thrust Bearing, Balls between Flat Plates. 

When nd = 3 5 7 9 10 

P, safe, in lbs. = 475 1,200 2,200 3,200 5,000 


Thrust Bearing, 2 Point (Balls in Races of Larger Diam.). 

When nd — 3 6 8 10 12 14 

P, safe, in lbs. =300 800 1,500 2,750 4,000 4,800 

Relation between Ball Diam. ( d ) and Shaft Diam. (D). 

Three-point Thrust Bearing, d = 0. 143 44). 17D 

Flat-plate “ “ d = 0.125 + 0.19D 

Two-point race “ “ d = 0.0625 + 0.166D 

Radial, four-point. “ <2 = 0.3D, when D^.1.5 in. 

“ “ . “ <2 = 0.31 + 0.15D when D> 1.5 in. 


The foregoing proportion represents the practice of the American Ball 
Co., of Providence, as derived from their catalogue by the author and 
may be taken as guidance in design. 

Friction of Ball Bearings.. M. I. Golden (Trans. A. S. M. E.) from 
experiments on balls from | to £ in. in diam. in radial or annular bear 
ings at, speeds from 200 to 2,000 r.p.m., deduces as a tentative formula’ 

Friction = Load ^0.005 + ^ +0.005Z)) , where <2 = diam. of ball, and 

20 = diam. of path of balls in the races. 

At speeds around and exceeding 2,000 r.p.m. chattering takes place, 
which may be reduced to a marked degree by the use of oil. He found 
g = 0 00475 (taken as 0.005 in formula). 

Double Ball Bearings. In an ordinary ball bearing the turning of 
the shaft rotates the balls in such a manner that the surfaces of two con¬ 
tiguous balls rub or grind upon each other, and this is said to be tb,e cause 
of a large proportion of the failures recorded in the use of ball bearings. 

In the Chapman double ball bearing a smaller ball (not in contact with 
the shaft) is introduced between every two balls of the bearing proper, 
and a rolling contact throughout the bearing is thereby established. The 
Chapman Co. (Toronto, Out.) claim to save 80% of the work lost in fric¬ 
tion by ordinary self-oiling journal bearings, and refer to runs of 1£ to 2 
years duration without lubrication or appreciable wear. 







gearing. 


49 


GEARING. 

Spur Goars are toothed wheels for transmitting power between parallel 
shafts, the teeth being parallel to the axes of the wheels They are equiv¬ 
alent to friction cylinders or' discs having teeth provided to a\ oid slipping 
with heavy loads and, with an infinite number of teeth, the gears would 
become smooth-surfaced cylinders engaging with each other at their cir¬ 
cumferences These circumferences are called pitch circles and the 
velocity relation between any two wheels is determined from their respec¬ 
tive pitch circle radii c ,, ,___ 

For transmitting perfectly uniform motion the curves of the teeth a e 
specially formed, the condition for such motion being that the normal 
to all surfaces of contact between the teeth must pass through the meeting- 
point of the two taqgential pitch circles. . * 

Epicycloidal Teeth ior wheels are formed as follows, the pait ot 
tooth curve outside of the pitch circle is the path of a point on the cir¬ 
cumference of an arbitrarily chosen circle which rolls on the outside of 
the pitch circle, and the part of tooth curve inside the pitch circle is the 
path of a point on the circumference of the same arbitrarily chosen cncle 

when rolling inside the pitch circle. > , • i . i* 

For racks the pitch circle (of infinite diam.) becomes a straight line 
and the tooth outlines are generated by a point in the circumference o 
■a. circle rolling on the line above and below . 

Where gears are to work interchangeably the same rolling circle must 
be used throughout. Teeth should be designed so that at least two pairs 

aF III volute l Te etlf possess an advantage over epicycloidal teeth m that 
the distance between the wheel centers may be slightly varied without 
affecting the accuracy of contact; they are generated as follows. Diaw 
pitch circles and connect their centers. Through point of contact ot 
circles draw a line inclined at an angle of 75 to the l 11 }® of centers and 
from each center draw a circle tangent to this line. These circles are 
base circles and the tooth curve in each wheel is the path made by a point 
in I line unwrapped from the base circle of that wheel. The prolonga¬ 
tion of the outline inside the base circle to depth of tooth is a radial line. 
Diam of base circle = 0.966 X diam. of pitch circle. Involute rack teeth 
have straight outlines which make an angle of 7o with the pitch hne. 
Circular Pitch (p") is the distance on the pitch line between the centers 

.. TrXdiam. of pitch circle 
of two successive teeth, p — No. of teeth 

Diametral Pitch (. pd "), or the number of teeth per inch diameter of 

o,-tch circle = — • ° f teet - = -7 -r-TI' Used iargely in cut gearing. 

pitcn circle diam. circular pitch . , , ,. • . 

Proportions of Teetli. If diam. of rolling circle for generating epi 
cycloidal teeth is taken equal to 1.75 Xcirouiarpiteh, the tooth out iim 
from pitch circle to bottom of tooth in a pinion of 11 teeth will be a radial 
line. Addendum (or radial height of tooth outside pitch circle) 0.3p , 
Dedendum (or radial depth of tooth inside pitch circle) —0.4p ; hen e, 

Thickness of tooth on pitch circle = —p"; 

21-19 „ p" 


total length of tooth = 0.7p' 


space between 


, 21 ,, 
teeth = ^p ; 


backlash : 


40 


V 


'20 ’ 


clearance 


(0.4 —0.3)p" =—• The foregoing for cast wheels. For cut gears sub¬ 
stitute 0.3, 0.35° 0.65, 0.485, 0.515, 0.03, and 0.05, respectively, for the 

ab IMam2 f rai e pUch Formulas' } for Small Gears (Brown & Sharpe 
Mfc Co) Let P = diametral pitch; D ', d' —pitch circle diameters, 
Dd = outside diameters; N, n = nos, ? f teeth;. V, v = velocity ratios 
(’ D itals for gear and small letters for pinion engaging with same), o-dis- 
iance between centers of wheels; 5 = no. of teeth in both wheels. Then, 

' . _D' + d^J L . N= nv = J^. n = NV_ bV — 

b — 2 aP , d cf 2P 1 V v 4- V ’ v 


NV 


PD'V ^ 2a(N + 2). 2q(n + 2) 




n 


n 


D = 



PD’V nv 
V “ N> 


^ „ 2a V 

D' = — T v; d =• 

v + V v+V 
















50 ENERGY AND THE TRANSMISSION OF POWER. 


For a single wheel (in addition to foregoing lettering), let 1 = thickness 
of tooth or cutter on pitch circle; D" — working depth of tooth; s — adden¬ 
dum; / = amount added to tooth depth for clearance; D" + f — total depth 


of tooth; 
£P= DN 


P'— circular pitch. 
N „ N+2 


D 


= />' + —• 
1 p > 


Then P = — + - 2 = — = — • p' _—. 

men, r D /)/ p , , 1 - p , 

PD- 2; 


D" = =2s\ 


/=-*-• t = ^ 
' 10’ P 


D 


1 P' D’ 

5 =p =T= 0-3183P '=w =wT2-’ s 


N = PD' 


N + 2~P’ ~ P 

P^ 

2 7 P * N N + 2’” ,/_ P 

= 0.3685P'. 

Revel Gearing is used to connect shafts whose directions meet at 
any angle. 1 he pitch surface of each gear is the frustum of a cone, both 
cones having a common vertex. The teeth have their surfaces generated 
by the motion of a straight line traversing the vertex while a point in 
the line is carried round the traces of the teeth on a conical surface, which 
surface is generated by a line drawn from the extremity of larger diameter 
, pitch surface frustum to the axis and perpendicular to an element in 
the pitch surface. 

Spiral Gears are used to connect non-parallel shafts which do not 
intersect. Let a = angle of inclination of axes, and y, v, n, R, N, t, and T 
be respectively the pitch angle, circumf. velocity, revolutions, radius, 
no. ot teeth, circumferential pitch, and normal pitch of wheel A, and 
7if v it nu etc., similar values for wheel B. 

Then, r + n+«=180° and ^= sir Ul whence gi=- gsin r - 

® sinn n Pi sin n Ni 

T = t sin y and T\ = t\ sin n, and as T must equal T u — = s | n n . For mini¬ 
mum sliding make r = n- The position of the common "tangent at point 

of contact of the pitch cylinders is determined from-yy = —4-cos a) 

. Pi cot n \ n / 


(ni"*" COSa )* ^ so » cot y 


sin a 


n I 

-rcos a 

n i 

For a = 90°, — = cot y, or, ^^Y^OoffoU owbt 
W n , m „ . n _ revs, (m) of driver 1 r% 

Worm Gearing. In this case a = 90°, N= 1 and the teeth of B are 

inclined at an angle y to the edge of wheel, and tan y — ~— =0.15916— • 

, strength of Gear Teeth (Wilfred Lewis). Load in lbf transmitted 
by teeth, II fp by, where b— width of tooth face, and n = a factor depend¬ 
ing on the no. of teeth (n) and the curve employed. 

y, for involute teeth, 20° obliquity = 0.154 — 0-912 


n 


15 c 


teeth with radial flanks = 0.075 


(and epicycloidai) = 0.124 
0.276 


0.684 


n 


Safe Working Stress, f, in lbs. per sq. in. 

Speed of teeth in 

feet per min. 100 250 500 1,000 1 500 9 0 00 

Steel, /= 20,000 14,000 11.000 7,600 6 oqo 5 400 

Bronze, /= 15,000 10,500 8,200 5,700 feoo 4 000 

Cast Iron, /- 8,000 5,600 4,400 3,000 2,500 2 900 

n^°^ te i Strength. Safe load W, in lbs. 

in lb^5T V to ed n f 4°x(,»" n (l’„T ) T fc k ^ 
as m St a ”r?n“"‘ maker ' h ° WeVer ’ States that ™whid e g 'ha S 

Bevel Wheels. W fp"by x sma11 diam. of bevel 
, large diam. of bevel 


-300bp" for 


2,500 
4,800 
3,600 
1,900 

C. I. 














BELTING. 


51 


H.P. Transmitted = (TEX velocity of teeth in feet per min.) : 33,00(h 
Safe Maximum Speeds. 1,800 ft. per min. for teeth in rough, cast 
(iron) wheels; 2,500 ft. for cast-steel anti 3,000 ft. for machine-cut cast- 

Proportions of Gears. Face, b = 2p" to 2.5 p"; thickness of rim —■ 

0 4p" +0.125 in. at edge (add 25% for center); thickness of nm on beve 
wheel (larger end) = 0.48;/' + 0.15 in. (taper to vertex); width of oval 
arms (in plane of wheel) = 2,/' to 2.5p"; thickness of oval arms (par¬ 
allel to shaft) = v” to 1.25p". or half the width of arm; No. of arms- 

0 55^/No of teethX^T 7 ; taper of oval arms:— 2 p" to 2.5p" wide at 
hub end tapered to from’1.33;/' to 1.66p" at rim; thickness of hub = 
^4-0.4 in.; length of hub = 6 to 1.255. For arms of cruciform section, 
width of webs in plane of wheel = 2p" to 2.5 p ; width o we , ' iri 
of shaft = 5 to b + 0.08p"; thickness of webs in plane of whee 1-0.035* 
(No. teethNo. arms); thickness of webs in plane of shaft _^ min No 
Driving Chain. Allowable velocities = 500 to 600^ ft. per ^m. . 

of teeth in sprockets = 8 to 80. Radius of sprocket = P -2 sin (180 . No. 
of teeth) p" = length of chord bet. centers of two adjacent teeth. 

The Renold Silent Chain Gear consists of a chain made of stamped 
linkfof a peculiar form which runs on an accurately cut sprocket wheel. 
These links are joined by hardened-steel shouldered pins and are pro¬ 
vided with removable split bushings. Advantages: high speeds (up _ 

2 000 ft oer min.); largest size (2 in. pitch, 10 in. wide) transmits 126 H.P. 
at 1 000 ft per min.; positive velocity ratio; can be used <?n short centers, 
fn damp orTot places, runs slack, thus obviating excessive ^oumd fng 
iV ". contact is rolling instead of sliding and the running is pracucany 
SleS °No“oVteeth,> to 120. Where load or power .s pulsating. a 
spring center sprocket is used to absorb the shock. 

belting. 

r»n neeount of slip belting does not transmit power at an exact velocity 
ratio buUUs nealfy noiselfss and can be used over distances not exceed- 

‘"bIu Tension” 1 In‘t£y‘ ‘belt* strained ' around a pulley and in motion 
^fcSfflln? o°/ beta on 

rfn^leather-botuuned 1 pulleye^fo/limnp "roptf S K ,-««« 

t0 The 8 'Drlvlng Pull of a Belt _ TV - 1 «. and the 

Horse-Power Transmitted = ( 33000 / V ~ 33^000 '* 

-h in. in thickness; double beltS g from # i x * No . q{ . pliesX wi( lth in in. 
fiC Tension 6 in^Belts due to Centrifugal Force (unimportant at low 
speeds). /f=i^- 2 (where w-weight of 1 cu. in. of leather = 0.0358 lb.) = 

0.0134r 2 , and total tension on tight side Tensi^ 0 changes from Tn to tn 
Creep, Slip, and Speed As the e ^^^fwhichTs due to the release 
a slight retrograde movement,! f u Pj. ulley to revolve at a correspond- 

inVfy n dee n reased W rat C e This result, is called the slip, and the loss amounts 
to about two per cent. „ s 0 f 4,000 ft. per min., at which 

speM 8 — TS&SZ Breeds however rise as high as 6,000 

ft. per min. 









52 


ENERGY AND THE TRANSMISSION OF POWER 


II. P. of Belting (approximate formula). 

HP — Jet W1 ^ t,1:t i n in-X p ulley diam. in in. X revs, per min 
. . ' ' 2,800 for 
be ^'(r ,ff°««n uble , b f] ts divide by 1,960 instead of 2,800. 

Lengthen feet =L.) d r ° Per 1>lstance between Shafts. (Sag in in. = «; 

' Narrow belts over small pulleys, A = 15 ft., s = 1.5 to 2 in • wider belts 
over larger pulleys A = 20 to 25 ft., s = 2.5 to 4 in.; main belts over very 
large pulleys, A = 25 to 30 ft., « = 4 to 5 in. y 

Length of Belts. Open belt: L = tc'(R + R 1 ) + 20(R-R 1 ) + 2Z cos /?; 

Crossed belt: L=2(R + R 1 ) +/}') +21 cos /}; where L = length of belt 

m in., R and i?i = radii of larger and smaller pulleys, respectively B — ansle 

S^sX^lf^ in Pa eten ^ and f en , ter hnj’of Seys C^No^f 
pufleyJ in in. 80 ’ circular measure), / = distance between centers of 

’n ( ° Pe ? be , lts); The len ^ th of b ^t must be the same for 
each pair of pulleys in the set, and tne radii of the pulleys have the 

(1 01414® + cKYo°04724f+ir a / 0 h 4 ' 4(+ fi )K | _ i* 1 °? 4724Z + «)#-0.51657/^ 
™ i » r 04 24/ + <d - 1 being fixed by the design, insert values 

the^rad^ S'r* AW ° ne pai f, of pu ! le ys and solve equation for c. Let 

Ron^ 1 ^^ -a limit^fncluding^ail pTactical'arjrJhca 8 

T el n ^°r denvation see article by the compiler in Am. M^ch i 19-04 ) 

of L coLv»r ey ::^^ 

between any two successive speeds, a- y/ Hi, (geometric ratio). If a 

sSS «F Xft Kss 

side running on pulley. (5 = width^S ini sh ° uld not crossed on the 

leatlter. Leather should not be exp 

PULLEYS. 

of < belrf^£thicUes? d l,fr°m P a“ 11 Siter - ^0 d 2 h tO f n n 9?r It i O u liXwidti 

hub, -0.75Ato h; (-length of hub, -6; n-numbefSi aims f-width 
of arm at center of hub; h,-width of arm at rim, -0.8A; ». 25+ I 
h _ b_ . r . 26’ 

* ~ 4 + lOn + 0 ' 25 ln - Thickness of arms at hub and rim = ~ and & respec 

&„e <T set *"*»• "* h “>» 

with dimensions for each as above exceDtfnir tZT * Pulleys combined, 

of rimiaow! 0 80% of ,he ™>' ues &»* 

Wheel, together at 

of fnotion, =0.15 to 0.20, metal on metal 0 9W f n C Qo° n ’ ^coefficient 
0.2o, leather on iron; 0.2, wood on compressed paper ’ W °° d ° n metal; 





HOPE TRANSMISSION. 


53 


Fn = ptP ; H.P. = FnV = 33,000. Transmits power without jar, but is 
limited to very light loads. 


HOPE TRANSMISSION. 


Wire Rope. Used where belting is impracticable, for spans of 70 to 
400 feet. Ropes used are 6 strand, 7 to 19 wires per strand. The sheave 
pulleys have a deep V-groove with a rounded bottom of alternating leather 
and rubber blocks. The minimum diameters of sheaves for obtaining 
maximum working tension in rope without overstraining by bending 
are 150c?, 115c?, and 90c?, for ropes of 7, 12, and 19 wires per strand respec¬ 
tively, where c? = diam. of rope in in. Actual H.P. transmitted = 3. ld 2 v, 

•where sheave diams. are A. above values. Proper deflection in feet = 
0.0000695(span in feet) 2 . 

Speeds from 3,000 to 6,000 ft. per min. (v=ft. per sec.) 

Manila Rope. 




Diam. in in., d = 
Lbs. per 100 ft; = 


i 

9.5 


t 

16 


t 

20 


$ i h h n if 

30 34 42 50 70 112 


2 

130 


2f 

170 


2* 

192 


Ultimate strength in lbs. = 9,000c? 2 . Safe tension, Tn on driving side : 


wv- 


180c? 2 (lbs.). Centrifugal force, F = —^~, where w = weight ,of 1 ft. rope. 
H.P. transmitted = ^ ’ where n = No. of wraps of rope around 


pulley. Best economical speed = 5,000 ft. per min. Add 250 ft. of rope 
to calculations to provide for tightener. Sheave dimensions; pitch 
diam. = 40c? to 80c?; outside diam. = pitch diam. + 2d + rs in., center to 
center of grooves = 1 .5c?; center of groove to edge = c? + T5 in. 

Cotton Driving Rope transmits about -§■ more power than Manila 
rope for the same diam. Sides of pulley groove are inclined at 45°; dis¬ 
tance from center to center of grooves = 1.5c?; width of groove at out¬ 
side diam. = 1.25c?. The bottom of groove is rounded with circle of diam. = 
0.66c?. 

, w Tj^ 

Sag, s (in inches) is obtained from the following formula; Tn = -^~ + ws, 


for driving side, also tn 
span in feet. 


(= —+ e) ws < where L = length of 


wL 2 


FRICTION. 


The tractive force necessary to overcome friction between the surfaces 
of solids depends (1) directly on the pressure between the surfaces in 
contact; (2) is independent of the area of the surfaces in contact, but 
increases in proportion to the number of pairs of surfaces; (3) is independ¬ 
ent (at low speeds) of the relative velocity of the surfaces; (4) the trac¬ 
tive force depends on the coefficient of friction, pi, for the particular 
materials employed. 

Tractive force, Fn — pxP. 

Coefficients of Friction, pi, for Plane Sliding Surfaces (Morin). 

(For low speeds and light loads only.) 

Lubrication. 


Pol- 



Dry. 

Water. 

Olive- 

oil. 

Lard. 

Tal¬ 

low. 

Dry 

Soap. 

ished 

and 








greasy. 

Wood on wood.... 

...0.5 

0.68 

• • 

0.21 

0.19 

0.36 

0.35 

Metal on wood. . . . 

. . . .6 

.65 

.1 

.12 

.12 

• • • • 

.1 

Hemp on wood. . .. 

... .63 

.87 





.28 

Leather on wood. . 

. . . .47 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

Stone on wood. . . . 

. . . .6 







Stone on stone. . . . 

... .71 







Stone on W. I. 

... .45 


.12 


.11 


.15 

Metal on metal. . . 

. . . .18 

• • • • 

. 1 

• • • • 

Leather on iron. . . 























54 ENERGY AND THE TRANSMISSION OF POWER. 


Values of /i for Static Friction (Broomall). 


Steel on steel. . 
Steel on C. I.. . 
Steel on tin. . . . 
Pine on pine. . . 


Dry. Wet. 

0.4408 

.23 

.365 

.474 0.635 


Dry. 

C. I. on C. 1. 0.3114 

C. I. on tin.454 

C. I. on pine.47 


Wet. 

0.3401 


» = tangent of the angle of friction, i.e., the greatest inclination possible 
before sliding occurs. 

If surfaces are thoroughly lubricated the friction is neither solid nor 
fluid but partakes of the nature of both. 

Comparison of Solid and Fluid Friction. Solid friction varies 
directly as the pressure and is independent of the area of surface and of 
velocity (when low). Fluid friction is independent of the pressure, varies 
directly as the area of wetted surface, directly as v (at very slow speeds), 
as v 2 (at moderate velocities) and as v 3 (at high velocities). For low 
speeds Morin’s table may be used. For flat surfaces, 400 to 1,600 ft. per 
min., C. I. on C. I., lubricated, a = 0.23, at a pressure of 50 lbs. per sq. in. 

Friction of Journal Bearings (Beauchamp Tower). tl = c \ / v^p, 
where v = linear velocity in ft. per sec., and p = pressure in lbs. per sq. in! 
of the projected area of journal. (Projected area = length Xdiam.). 
Values ot c vary according to the lubricant employed, viz.: Olive-oil 
0.289; lard-oil, 0.281; mineral grease, 0.431; sperm-oil, 0.194; rape-oil’ 
0.212 ; mineral oil, 0.276. These values are for thorough bath lubrica¬ 
tion. To avoid seizing, p should not exceed 600 fbs. per sq. in. 

A roughly accurate expression for the coefficient of friction for machinery 
oil, deduced from the experiments of Tower and Osborne Reynolds, is 
(for speeds over 20 ft. per min.): 


fi— l-S^Ai-T- 6p, where v=surface speed in ft. per min., 

0 = excess of oil temperature above 60° F., and p— bearing pressure 
in lbs. per sq. in. 

The proper length for a lubricated bearing in which the bearing pressure 
shall be less than that required to squeeze out the oil film is l = P = 80(dN)i. 
where Z is length in in., d=diam. in in., P=total load on bearing in lbs., 
and A — r.p.m.—(J. T. Nicolson and Dempster Smith, in The Engineer, 
London, Nov. 23, ’06, and Feb. 8, ’07.) 

The following results were obtained by Prof. A. L. Williston (E. W. 
& E., 3-18-05). 


fi (average). 


Hyatt Roller Bearing.0118 

C. I. Bearing.0608 

Bronze Bearing.112 


Pressure per Sq. In. 

80 to 345 lbs. 

80 to 250 ‘ ‘ 

80 tod 45 “ 


The bearings were all 1* in. diam.X4 in., lubricated with moderatelv 
heavy machine-oil of good quality. The C. I. and bronze bearings were 
reamed to size and lapped to insure perfect surface and high polish, a at 
starting for the Hyatt bearing was found to be 0.0058 
Friction of Collar Bearings. 
n = 0.036. 

Friction Loss in Journals and Collars (P = outside or mean radius 
for journal and collar, respectively). Work lost, in ft.-lbs. per min.= 
T fi-k — X InKN , or, expressed in horse-power, H.P . =0 0001904uPPA 

Work Lost in Pivot Friction = (0.5 to 0.66)(2^PN^P) inft!-lbs7 


For p= 15 to 90 lbs., u = 5 to 15 ft., 


LUBRICATION. 

Spongy metals like C. I., brasses, and white-metal alloys, lessen fric¬ 
tional resistance to a considerable degree, but the use of unguents is neces¬ 
sary lor good results. Lubricants are solid, as graphite; semi-solid as 
greases; liquid, as oils. The following are the best lubricants for’the 
purposes indicated : 

Low temperatures: light mineral lubricating oils. 

Intense pressures: graphite or soapstone. 

Heavy pressures at slow speeds: graphite, tallow. 

Heavy pressures at high speeds: sperm, castor, or heavy mineral oils 












LUBRICATION. 


5 <3 


Light pressures at high speeds: sperm, olive, rape, or refined petroleum 

oils. 

Ordinary machinery: lard-oil, tallow-oil, heavy mineral oil. 

Steam cylinders: heavy mineral oils, lard, tallow. 

Delicate mechanisms: clarified sperm, porpoise, olive and light mineral 
lubricating oils. 

Metal on wood bearings, -water. 

Kssential Properties of Good Lubricants, (l) Body or viscosity 
sufficient to prevent contact of surfaces. (2) Freedom from corrosive 
acids. (3) As much fluidity as is consistent with body. (4) Low coeffi¬ 
cients of friction. (5) High flash and burning points. (6) Freedom 
from substances likely to cause gumming or oxidation 

Specific Gravities of Lubricants. Petroleum, 0.866; sperm-oil, 
0.881; olive- and lard-oils, 0.917; castor-oil, 0,966. 

Flashing and Burning Points. Sperm-oil flashes at 400° F. and 
burns at 500° F.; lard-oil flashes at 475° F. and burns at 525° F. 

Thorough lubrication (preferably the oil-bath) is essential in order to 
obtain the best results, and to prevent seizing. 

Graphite as a Lubricant. Foliated or thin flake graphite when 
applied as a lubricant materially reduces friction and prevents seizing 
and injurious heating of bearings. It may be applied dry to surfaces 
wnere pressures are light, or mixed with oil or grease (3 to 8% graphite, 
by weight) for heavy pressures. It may also be used to advantage in 
the presence of high temperatures, as in steam, gas-engine, and air-com¬ 
pressor cylinders, and also in ammonia compressors and pumping-engines. 
Water of condensation often suffices for a mixing lubricant. 

Graphite fills up the minute depressions and pores in metal surfaces, 
bringing them much nearer to a perfectly smooth condition so that a 
considerably thinner film of oil (which may have a greater fluidity than 
usual) will be sufficient. 

A test of car-axle friction by Prof. Goss (bearing pressure 200 lbs. per 
sq. in.) gave the following results- 

Sperm-oil only, 9 drops per min., rise in temp, per hour = 26° F.; /( = 0.284 
Sperm-oil with 

4% of graphite, 12.9 “ “ “ “ “ “ “ “ =28° F.; g =0.215 

(From catalogues of the Jos. Dixon Crucible Co.) 

Power Measurement. Power is measured by dynamometers, which 
either absorb or transmit the power undiminished. The Prony Brake is 
the typical form of absorption dynamometer and consists of a horizontal 
lever connected to a revolving shaft or pulley in such a manner that the 
friction between the surfaces in contact tends to rotate the lever-arm in 
the direction of the shaft rotation. This tendency is resisted by weights 
on the lever-arm, and the weight that will just prevent rotation is ascer¬ 
tained. Let P = weight in lbs. on lever, L = length of lever in feet from 
center of shaft to point of application of weight, V = velocity in ft. per 
min. of point of application of weight if allowed to rotate at the speed of 
the shaft, )V = r.p.m., and W = work of shaft or power absorbed per min. 

Then, W=PV=2xLNP ft.-lbs., or, H.P. = |^^. 



HEAT AND THE STEAM ENGINE. 


Heat, according to the dynamical theory, is a mode of motion of the 
molecules of a substance, its intensity being proportional to the amount 

of th?subsTance S m ° St readl y observed effect being that of the expansion 

Transfer of Heat. Heat will pass from the warmer of two bodies 
to the colder until their temperatures become equal, the transfer being 
effected by radiation, conduction, or convection. 

Radiation is the transfer of heat from one body to another across 
an intervening medium whose temperature is not affected by the transfer, 
Dark, rough surfaces are the best radiators and are advantageous in 

P Ba r i«Hli° r w h ®. atl ? 4 g ’ w, lV le , ,lght - P° Iished surfaces are the poorest. 

w. Radia n^ Values. Lampblack, 100; polished metals 
Ca& Tii i P+ 1 tt^-V w X, ou £.ht iron, 23; steel, 18; brass, 7; copper, 5; silver, 3 
iof e r ff l ni s Radiated per Hour per Square Foot of Surface (for 
nn^ 97 lff f- renC no?, tem P eratUr , e) b Polished metals: silver, 0.0266; copper. 

■m" 7 [) nS’ °n!h 4; zm ? a T br t ss ’ °; 0491: tinned iron, 0.0859; sheet 
non 0 .092. Other materials sheet lead. 0.133; ordinary sheet iron- 
O.o66, glass, 0.595; cast iron, new, 0.648; do., rusted, 0.687; wrought- 

1.0853- P oil °1 6 4^ W °° d ’ St ° ne ’ and bnck ’ °- 736 : sawdust, 0.72; water. 

th f transf , er of heat by contact between the molecules 
of a body or the surfaces of contact of two distinct bodies. 

Relative Values of Good Conductors. Silver 100- cornier 73 6- 

bSSth?1. : 8;““wato^ : 0.147' 1U>i *‘* t ' 11 lead ’ 8^'Platinu m. SA\ 

These values are for bright surfaces up to f in. thick. For surfaces coated 
with grease or saline deposits (i.e., condensers) Whitham states that these 
values should be multiplied by 0.323. 

Relative Values of Poor Conductors as Heat Insulators ♦ Min. 

eral wool, 100; hair-felt, 85 4; cotton wool, 82; sheep's wool, and in¬ 
fusorial earth, 73.5; charcoal, 71.4; sawdust, 61.3; wood and ki?-space, 

Comparative Radiation from Covered Pipes. Bare nine i on- 

covering of magnesia + 7% asbestos, 0.308; plaster of Paris+ 4^ asbestos! 

Radiation from Bare W. I. Pipes in B.T.U. per sq. ft. per hour 
mediunf(taken'af”) tem P erature between pipe and surrounding 


Degs. diff. 

Radiation. 

10 

0.743 

50 

0.816 

100 

0.911 

150 

1.035 

200 

1.167 

250 

1.22 

300 

1.32 


Radiation and Convection 

Still Air. 

Moving Air, 

1.247 

1.583 

1.55 

2.038 

1.773 

2.344 

1.983 

2.615 

2.18 

2.856 

2.4 

3.12 

2.6 

3.37 


+ k^ t L eai yf Pil>e u°Y e * inSS ?, Th e following figures are for coverings 1 in 
thick. (For each Tj j in. additional thickness (up to 1 5 in ) subtree* ti?' 
percentage given.) Under average conditions (air at about 70°, steam about 

56 








measurement of heat. 


57 


100 lbs. pressure) 1 sq. ft. of bare pipe will give off about 3 B.T.U. per 
hour. 

B.T.U. radiated per hour per sq. ft. of surface for each deg. F. difference 
in temperature between steam and outside air (approx.) ; 

Hair-felt, 0.3/5 (2.5%); Remanit, 0.415 (2%); Manville sectional, 
best, 0 5 (1.4%); Magnesia, 0.515 (5.2%); Asbestos sponge, felted, 0.575 
(9.2%); Asbestos air-cell, 0.675 (12%); Navy asbestos, 0.7 (8.4%); 
Asbestos fire felt, 0.745 (11%). ’ 

Coverings of 85% magnesia and solid cork coverings (1 in. thick) save 
about 83% of the heat that would be radiated from a bare pipe. Remanit 
(carbonized silk, wrapped) saves about 87%. 

Convection is the transfer and diffusion of heat in a fluid effected by 
the motion of its particles. Water in the bottom of a vessel, or air on the 
floor of a room, being heated, becomes lighter and rises, allowing colder 
fluid to take its place. Convection currents being thus formed the heat 
is distributed through the fluid. 

Expansion results from the application of heat to all bodies. (For 
coefficients of linear expansion see foot of page 18.) Water between 
32° and 39.1° F. is an exception to the general law; it contracts as the 
temperature increases. Cast iron, bismuth, and antimony expand when 
solidifying, while gold, silver, and copper contract. 

Measurement of Heat. Temperature is a measure of the intensity 
of heat and is determined by the employment of a thermometer or a 
pyrometer. 

Thermometers. The freezing- and boiling-points of water (under 
atmospheric pressure) are marked on all thermometers, the space between 
being graduated as follows; 

"\T f 

System. Divisions. Freezing-point. Boiling-point. 


Fahrenheit (F.). 180 32° 212° 

Centigrade (C.). 100 0° 100° 

Reaumur. 80 0° 80° 


whence F° = 1.8C.° + 32 and C.° = i(F.°-32). 

Pyrometers are used to measure very high temperatures, Le Chatelier’s 
being a thermo-electric couple of platinum and platinum-rhodium alloy 
employed in connection with a galvanometer and calibrated scale. The 
high temperatures of furnaces may be approximately ascertained by 
means of the copper cylinder pyrometer. A small copper cylinder of 
weight w (specific heat = 0.0951). is allowed to attain the temperature 
t° of the furnace and then plunged into a known weight, w\ of water whose 
initial and final temperatures are t °i and T° respectively. Then, 
„ wi(r°-o 0 )+o.o95i?r:r o 

1 0.0951u> 

Heat Units. The heat motion in a body depends on its mass, heat 
capacity, and temperature. 

The British Thermal Unit (B.T.U.) is the amount of heat required 
to raise the temperature of one pound of water through one degree 
Fahrenheit, the water being near the temperature of its greatest density, 
39.1° F. One B.T.U = 778 ft.-lbs. of energy. 

The Calorie (metric system) is the amount of heat required to raise 
one kilogram of water one degree Centigrade at or near 4° C. 1 B.T.U = 
0 252 Calorie (Cal.). 1 Cal. =3.968 B.T.U. 1 Cal. = 426.8 kilogram-meters = 
3087.1 ft.-lbs. 

Specific Heat. Bodies, weight for weight, vary in their capacities 
for absorbing heat. If the heat-absorbing capacity of water is taken 
' as unity, the relative capacity of another substance is called its specific 
heat and is therefore equal to the amount of heat in B.T.U. required to 
raise the temperature of one pound of the substance through 1° F. 

Specific Heats of Various Substances. Water at 39.1° F., 1.00; 
water at 212° F., 1.0132; ice at 32° F., 0.504; mercury, 0.0333; cast iron, 
0.1298; wrought iron, 0.1138; steel, 0.117; copper, 0.0951; coal, 0.24; 
tin, 0.0562; lead, 0.0314; glass, 0.1976; brass, 0.0939; coal ashes, 0.215. 
Gases (under constant pressure) carbonic oxide, 0.2479; carbonic acid, 
0.217; ammonia, 0.508; air, 0.2375; hydrogen, 3.409. 

Expansion of Gases. Marriotte’s Eaw. The volume of a given 
portion of a gas varies inversely as its pressure, if the temperature be con- 







58 


HEAT AND THE STEAM ENGINE. 


stant. Vco 


1 


V = 


a constant ^ and py = Si constant. The pressure 

c'mve of'a fas expanding aLrding to this law is a rectangular hyperbola 

and is called the ^sotliermal o_ ncr ga^ volume of a g ive n portion of a 

Gay-Lussacs the increase in temperature if the pressure be con- 
gas varies directly as the ‘ be respectively the original volume the increase 
stant. Let \ , V\, ana > 2 ' j t o tbe r j se j n temiierature. Ihen, 

J°i ume ’ q where « = coefficient of cubical expansion ( = coeff. 

oV ImeaTfxUns^Xs');" V,~ V+ V, - F+ VaT - V(1 +«C). » for a.r 

"ISntf TemSfaturer If a given volume of air at 32° F be reduced 

Absolute ie p _ nn f 12036111 its volume will theoretically 

491-13° m temperature Considered as having ceased 

become zero and its neat i y below the melting-point of 

For a perfect gas, absolute ze_ ^ ^ hich po i nt all tempera- 

ice, or, practically, -461 /* r JlL a j i\ gases liquefy before reaching 

absolute°zero.k e At^^ute < Temperau!re^'(r^=4(pl^+ reading (( | thermometer 

Combination of Marrl.tte-s and Gay-I-ussac-s 1-w.^Prcon- 
stant, and PVx-c, -• r V n • _ j n =2,116.5 lbs. per 

sf d 7t.fTF-12!38r><2,nl5-26 217 66 ft.-lbs.-Sr, and, as r-493°, 

fi l 5 a 3 tSt 4 'Heat. Ir -‘“7^ ^ Slit™ Sy 

th^pohitfof fusion a'nii of eo^ljotathini and at^th^e pointa^ieaWs^absorbed 
to perform the work of mo.ecular ^ out in c hang- 

i,lg & onf pound of rteTubsta?ce from one state to another without altering 

itS Ta e t?nt r Heat'of Substances in B. T. U. per Lb. Fusion Ice, 142 6 
to H 4 iron 4F4 to 59.4; lead, 10 55 Eyaporat.on■ Water, 965.7. 

HxStl 5 ol 9; an b rSgV„!n b t^' Mtn^said to occur when 
i , S ?k h p at reouired for steam has been taken up. Boiling occurs 

al f th til^tpnsion in the water overcomes the surrounding pressure. Dry 
when the tension m ine waic snecific volume, temperature and 

saturated steam is that whi , e formation. Wet saturated steam 

pressure corr * s ^ the water from which 

it is^eneratof. 88 Superheated 1 steam is. that which has its temperature 

'Tpecific 0 '"volume -N^ ^of'““‘t^penb.' Specific density-No. of lbs. 

‘“Moisture In Steam is measured by a calorimeter, and the percentage 

of moisture, a»-100x " - L - " licre W “ t0tal 1,eat ' Z '“ latent 

i f lb nf steam at the pressure of the supply-pipe, H\ - total heat 
per ft. at the pressure of the ot °JhT&lrfeSlxXated 
Km^rSfcaSmS-and ^-Kerature duo to the measure on 

th AU i bu h tTto S I% of removed by the use 

L = latent heat of 1 lb. of steam at the observed pressuie 

tG, pressure ’a^id Temp^ratureT^eYations^f Saturated Vapor. 

?J = a + 5rt" + c/? n (Regnault). 


T° = observed 
Log 


32° to 212° Fo 
a = 3.025908 
log 6 = 0.61174 
log c = 8.13204-10 


212° to 428° 

3.743976 
0.412002 
7.74168-10 


32° to 212° 
log « = 9.998181—10 
log/? = 0.0038134 
n = t °-32 


212° to 428° 

9.9985618-10 
0.0042454 
£° —212 






SENSIBLE HEAT. 


59 


B C 

Rankine gives as a close approximation, log p = A -where 

A =6.1007, log £ = 3.43642, log C = 5.59873, and p = lbs. per sq. in. (in 
both formulas). 

Sensible Heat, — Heat of the Liquid (h). The number of B.T.U. 
required to raise 1 lb. of water from tne freezing-point to *° Centigrade = 
(* + 0.00002*2+0.0000003* 3 ) X1.8. 

The Total Heat of Evaporation is the quantity of heat necessary 
to raise one oound of water from 32° F. to a given temperature and then 
evaporate it. Total heat (in B.T.U.) = 1,091.7 + 0.305(*°-32) = 1,081.94 
-+-0.305*°. Latent heat = total heat —sensible heat = (approximately) 
l ,001.7 — 0.695(*° — 32). (For greater accuracy subtract the sensible 
heat as obtained from formula above from the total heat.) 

Density ( D ), Volume (F), and Relative Volume (F r ) of Satu¬ 
rated Steam. The density or weight in lbs. of 1 on. ft. of saturated 
steam may be obtained from log Z> = 0.941 log p — 2.519. The volume 
of 1 lb. of steam in cu. ft. may be obtained from log F = 2.519 — 0.941 log p. 
The relative volume or number of cubic feet of steam from 1 cu. ft. of water 
may be derived from log V r — 4.31388 — 0.941 log p. 

The External Work of 1 lb. of Steam, W e (in 
14 4n(cu. ft. in 1 lb. s te am at p, — 0.010) 

778 


where 0.016 = cu. ft. 


B.T.U.) = 
in 1 lb. of 


W3»tGr. 

Evaporation from and at 212°. In comparing the evaporative 
performances of boilers working under various pressures and tempera¬ 
tures, it is customary to reduce them to a normal standard efficiency 
expressed by the equivalent weight of water which would be converted 
into steam if it were supplied to the boiler at a feed temperature of 212° 
and evaporated at the same temperature and at atmospheric pressure. 
The equivalent weight of water evaporated “ from and at 212 , 

W = where H = total heat of the steam generated at the given abso¬ 

lute pressure (gauge pressure + 14.7 lbs.) and h = the heat of feed-water. 

Properties of Saturated Steam. The following table is abstracted 
from the complete tables of Prof. C. H. Peabody, whose results are probably 
in more general use among engineers than any others. H = total heat of 
the steam = 1,091.7+ 0.305(4°-32); /i = heat of the liquid; L = latent 

'P'U 

heat of vaporization, = 11 — h. Internal work, W X = L — where u = v — 
.016 = increase of volume of water and steam during evaporation (1 lb. 
wa ter = .016 cu. ft.). Entropy of liquid 


of vapor, 


L 


4>a—— + 4>w\ 


<biv = specific heat X log e —; 

ro 

t = *° + 460.7. p (absolute) = pressure 


entropy 

above vacuum in lbs. per sq. in.; v = vol. of 1 lb. of steam in cu. ft. 
w = weight of 1 cu. ft. of steam in lbs. The values above 325 lbs. pres¬ 
sure are from Buel’s tables. 

Cooling Water Required by Condensers. Heat lost by steam = heat 
gained by the water; or, lbs. steamX(sensible heat + latent heat —temp, 
of hot well) = lbs. waterX(final temp, of water—initial temp, do.), which 
may be reduced to. lbs. water per lb. of steam, w = (1 113.94 + .3057 , s 
— Th)-*-(Tu) — tw), where T s = fcemp. of steam at, release, f/t = temp, of 
hot-well (usually from 110 to 120° F.), Tw and *<*> = final and initial temps, 
of the cooling water. 

This formula has been criticised by E. R. Briggs (Am. Mach., 5-18-05) 
because it assumes that the whole weight of entering steam must give 
up its heat of vaporization at the release temperature, when, as a matter 
of fact, some 20 to 30% of the steam is in the form of water at this point. 
He suggests the following formula which gives much smaller results. 

( 2 *54'Vx 

H— '' ' ) -h (Tiv — hv), where 7/ = total heat per lb. of steam sup- 

plied to engine (reckoned above Th), x = steam consumption of engine in 
lbs. per I.H.P. hour, and 2,545 = B.T.U. in one H.P. per hour. 

Specific Heats of a Gas. The specific heat (k P ) at constant 
pressure of any normally permanent gas such as air is 0.2375 B.T.U. 






60 HEAT AND THE STEAM ENGINE. 


Properties of Saturated Steam. 


p (abs.). 

t° F. 

V. 

w. 

II. 

h. 

L. 

0.5 

80 

640.8 

.00158 

1106.3 

48.04 

1058.3 

1 

101.99 

334.6 

.00299 

1113.1 

70 

1043.1 

3 

141.-62 

118.4 

.00844 

1125.1 

109.8 

1015.3 

5 

162.34 

73.22 

.01336 

1131.5 

130.7 

1000.8 

10 

193.25 

38.16 

.02621 

1140.9 

161.9 

979 

14.7 

212 

26.42 

.03794 

1146.6 

180.9 

965.7 

15 

213.03 

26.15 

.03826 

1146.9 

181.8 

965.1 

20 

227.95 

19.91 

.05023 

1151.5 

196.9 

954.6 

25 

240.04 

16.13 

.06199 

1155.1 

209.1 

946 

30 

250.27 

13.59 

.0736 

1158.3 

219.4 

938.9 

35 

260.85 

11.45 

.08736 

1161 

228.4 

932.6 

40 

267.13 

10.37 

.09644 

1163.4 

236.4 

927 

45 

274.29 

9.287 

.1077 

1165.6 

243.6 

922 

50 

280.85 

8.414 

.1188 

1167.6 

250.2 

917.4 

55 

286.89 

7.696 

.1299 

1169.4 

256.3 

913.1 

60 

292.51 

7.096 

.1409 

1171.2 

261.9 

909.3 

65 

297.77 

6.583 

.1519 

1172.7 

267.2 

905.5 

70 

302.71 

6.144 

. 1628 

1174.3 

272.2 

902.1 

75 

307.28 

5.762 

.1736 

1175.7 

276.9 

898.8 

80 

311.8 

5.425 

.1843 

1177 

281.4 

895.6 

82 

313.51 

5.301 

.1886 

1177.6 

283.2 

894.4 

84 

315.19 

5.182 

.193 

1178.1 

285 

893.1 

86 

316.84 

5.069 

. 1973 

1178.6 

286.7 

891.9 

88 

318.45 

4.961 

.2016 

1179.1 

288.4 

890.7 

90 

320.04 

4.858 

.2058 

1179.6 

290 

889.6 

92 

321.06 

4.76 

.2101 

1180 

291.6 

888.4 

94 

323.14 

4.665 

.2144 

1180.5 

293.2 

887.3 

96 

324.64 

4.574 

.2186 

1181 

294.8 

886.2 

98 

326.12 

4.486 

.2229 

1181.4 

296.4 

885 

100 

327.58 

4.403 

.2271 

1181.9 

297.9 

884 

102 

329.02 

4.322 

.2314 

1182.3 

299.4 

882.9 

104 

330.43 

4.244 

. 2356 

1182.7 

300.9 

881.8 

106 

331.83 

4.169 

.2399 

1183.1 

302.3 

880.8 

108 

333.2 

4.096 

.2441 

1183.6 

303.8 

879.8 

110 

334.56 

4.026 

.2484 

1184 

305.2 

878.8 

112 

335.89 

3.959 

.2526 

1184.4 

306.6 

877.8 

114 

337.2 

3.894 

.2568 

1184.8 

308 

876.8 

116 

338.5 

3.831 

.261 

1185.2 

_ 309.4 

875.8 

118 

339.78 

3.77 

.2653 

1185.6 

310.7 

874.9 

120 

341.05 

3.711 

.2695 

1186 

312 

874 

125 

344.13 

3.572 

.28 

1186.9 

315 

871.9 

130 

347.12 

3.444 

.2904 > 

1187.8 

318.4 

869.4 

135 

350.03 

3.323 

.3009 

1188.7 

321.4 

867.3 

] 40 

352.85 

3.212 

.3113 

1189.5 

324.4 

865.1 

145 

355.59 

3.107 

.3218 

1190.4 

327.2 

863.2 

150 

358.26 

3.011 

.3321 

1191.2 

330 

861.2 

155 

360.86 

2.919 

.3426 

1192 

332.7 

859.3 

160 

363.4 

2.833 

.3530 

1192.8 

335.4 

857.4 

165 

365.88 

2.751 

.3635 

1193.6 

338 

855.6 

170 

368.29 

2.676 

.3737 

1194.3 

340.5 

853.8 

175 

370.65 

2.603 

.3841 

1195 

343 

852 

180 

372.97 

2.535 

.3945 

1195.7 

345.4 

850.3 

190 

377.44 

2.408 

.4153 

1197.1 

350.1 

847 

200 

381.73 

2.294 

.4359 

1198.4 

354.6 

843.8 

210 

385.87 

2.19 

.4565 

1199.6 

358.9 

840.7 

220 

389.84 

2.096 

.4772 

1200.8 

363 

837.8 

230 

393.69 

2.009 

.4979 

1202 

367.1 

834.9 

240 

397.41 

1.928 

.5186 

1203.2 

371 

832.2 

250 

400.99 

1.854 

.5393 

1204.2 

374.7 

829.5 

260 

404.47 

1.785 

.5601 

1205.3 

378.7 

826.6 

275 

409.5 

1.691 

.5913 

1206.8 

383.6 

823.2 

300 

417.42 

1.554 

.644 

1209.3 

391.9 

817.4 

325 

424.82 

1.437 

.696 

1211.5 

399.6 

811.9 

500 

467.4 

0.942 

| 1.062 

1224.5 

443.5 

781 

1000 

546.8 

1 0.48 

1 2.082 

1248.7 

528.3 

720.4 













































SPECIFIC HEAT AT CONSTANT VOLUME. 61 

bemg performed! 1 and equal*”* 0 V ?689 B T TJ * S IeRS ’ n ° external work 

Expressed^,, fo«,po«nd, .and ukuTcfpiS for 8ymb o.s, 

A p 184-/7 ft.-lbs., and At—131.42 ft.-lbs. 

peratures. External work & = P( F° PS p^ £J essure is the same at all tem- 
Total heat = Ap(n — t) ; .*. Internal work'll — RV 

° n ‘ J “^af’work is done, 

usuaily taken as o'-lSoF Grmdiey * tate-f 1 ha™if* cons, “ nt Pressure is 
(between 230“ and 246“ F.) to 0.6482 (between 295" Sd Iff" p i° m , 0 ' 4317 

absolute pressure in lbs ner in es ^P u - 4bJ + 0.001525p, where p = 
employs the following formula, where k P varies aTthe prelsure and^nvemefy 
as the cube of the absolute temperature: £* = 0.43 + 1,476,000^- (p in lbs 
per sq. in.; r =461° + t° Fahrenheit). T< * 

iiy making fair suppositions as to the temperatures invnl^P t 

Suref the valor"? if ree ++ "ithlw of Wnl For^ow 
nvesriaators whlff^ , 1{e « nault (0-4805) seems corroborated by thei 
taken. * ’ h1 f pressures around 120 lbs. a value of 0.6 may be 

5 ft p -?bs eat ^-t!r 8 5 ( .?| e s 3 ft -i b h s - “><1 

heat of superheated steam H, =// + /- it _A r p rf V + u‘\ ^he total 

■— - 

Expansion Curves. AdJabatics and Isothermals. The -iron 4 

is"' 1 P-fr C ( % ,ri>™ 

W?i e p; V ” °C T-7p 0 V 0, p eX vTt n n When ‘he ejtrve is E ofTie Llm 
stance employed fn^tle^paSnT^' ^ ^-(.K^K,,) of the sub- 

' hen a Sas expands against a resistance it performs work which reauires 
fIrn?> XPe b 1< ltU - re i° f beat. If the gas itself yields this supply of heat its 

semed r by r pF n -c ere if rhe { he expansion is called adiabatic and repre- 
rtilii f Dy ta e heat required during the expansion be sun- 

phed fiom an external source the temperature of the expanding gas remains 
constant and the expansion is termed isothermal (PV = C). 8 

Various Expansion Curves. Isothermal of a perfect gas- PV = C 

Adiabatic of a perfect gas: PF r = C. ( r = 1.3 for superheated steam and 
1.408 for air usually taken as 1.41). Expansion of dry, saturated steam 

S+035FF- I 0 i 4fl- t 3 h s e q r Tf -°k SUP h erh °f! ef ! ; PV { \=475 (Rankine), or 
\\%-C } w| 1PrP , ( nTvf rn) - A £ Jlabatlc ( I f saturated steam: 

V. ’ where n—1.0-55 +0.1 xdryness fraction, the dryness fraction 
Sf'fK the weight of the steam after the water particles are subtracted 
• u* the weight of both steam and water particles. n=1.135 for 

mSilL^RankS). ZeUner) W “ 1,111 f ° r steam contain ing 25% of 

(lor additional relations between p, v, and r see Compressed Air.) 
Specific Volume of Dry Saturated Steam. F=— + „. Take 

t° at 1°, find the increase of pressure p from tables for 1°. v =Vol of ] lb 
° x'r a / er ’ in ^“latent heat at r° F. (absolute), in ft-lbs 

than that ot saturated 

Thermal Efficiency of Heat Engines. Efficiency =^i, where r F 

the absolute temperature at which the heat is received (which should be 
as near to that of the furnace or gas explosion as possible), and rj the 






I 


HEAT AND THE STEAM ENGINE. 


62 

f-SHES w a? ss 

at the furnace temperature (the g f cooling water in the condense . 
ture of rejection is higher than that ote temperature to that of the 
Steim is not compressed from tne contie temperature correspond- 

fumfe only a small part being ,co^sed to the » to the 

ing to boiler pressure. I f the condense mugt be heated to boiler tern- 

boiler a corresponding weight of fee ‘ linder causes waste, only a por- 
nerature. Initial condensation in t e y ’ , d during the stroke, and 

tion of the steam so condensed bemg e- P the cy h n d e r requires an 
the expansion is not adiabatic. , r( ,ke which performs no work dur- 

additional amount of steam for Water particles in the steam 

ing the full pressure period denser without performing MOik 

(due to boiler priming) pass into t e <md their attemp t to vaporize. 

and also abstract heat ^ cylinder lubricant or the packing 

LTlt If fcffrS temperature^ of^ -^able^condens™ wa,er_ 

flo ' v “ d ot tho moving parts 

the engine) are additional causes of o.■ • steam is admitted to a 

Initial Condensation. When rteamjj. a of it con- 

cylinder which has been cooled to exha,ust■ . b ut, as the cylinder 

Senses After cut-off the the latent heat 

and steam temperatures become ™°* e f ation . The initial 

liberated during liquefaction causes a parua^ ered through the re- 

loss is c 9 nsiderable, and, bemg but partia^y ^ releaS6) part G f which 

evaporation, a quantity o , causes back-pressure. . . 

evaporates during the exhaust and cau.e. T jf th engine has 

Methods of Reducing Cylinder Condensation^ a iiow the 

a high rotating speed the time of Clothing 

temperature changes whlc V 11 ^‘„ materials is a partial means of preven- 
the cylinder with non-conducting ma ^ tQ t ’ he wal i s of the cylinder 
tion. The supply °f heat ^ . -Aiots re-evaporation providing that 

by means of a surrounding J - - nermit the absorption of the heat. By 

eompoundinS? C the S work is divided 1 

the re-evaporation taking place earher 

in Th e e t fe 1 oP S nper 0 h n eatecl steam is the^ effective*^eventive^con- 
densation. Saturated ste^ is ^owed t A suffici ?ntly raised by the 
form of superheater, its temperature Dei g ^ SQ) dunng the stroke, 

heat of the furnace gases to Jeep lubrication being impossible 

Superheat cannot exceed + 750 4.fS however, are obtained between 

700 ^ Whh superheat ^pressuresM? not ^ed to be^o^ngb 

in ^ ^ 

transmissions, and effects a saving of ? W> *o steam . consump tion 

;Vt 120 lbs. pressure, with 1/0 superneat, /o • f 50 % has been 
lias been ^ practice. 

^The following formutas approximately express the results of a large 
number of tests (S-saving in per cent): 


S = 5 17 + 0.083 X degs. F. of superheat (for turbines); 
c = 4 + 0 12 Xdegs. F. of superheat (for reciprocating engines). 

0.48TF(b°■ 


-< 2 °) 


Heating Surface of Superheaters. A (in sq. ft.) 6(t 3 -<i) 

where 0.48 = sp. heat of ^Perheatei^^temp.^fTi^supethettingt ^'temp. 

6-B.TjL transmitted per sq. ft. 
of heating surface per hour, where (h~ <i) -400 to ouu r. 




indicator diagrams. 


63 


tion«^n S ^ffL^ arly / ndependen u t of speec J of slidin e surfaces, is proper- 
nai to difference of pressure between the two sides of valve and is 

to'over^nV^f °Y erlap of . vah 'e. With well-fitting valves it may'amount 
to^'er 20% °f the entering steam, and rarely falls below 4%. 

™ y n J acketed cylinder with a given ratio of expansion, initial con- 
densation (expresseii as a percentage of the steam in the cylinder) diminishes 

5rnb f ”,‘1 temperature, while the total condensation per 

stroke increases with such temperature increase. 

D-roa ?pr V f °£ ^ given .^ ti i °, of expansion is as great, and sometimes 

W f°S JaC ^ et 1 as W1 , h them, showing clearly that the regenera- 

cylinder walls with a given ratio of expansion is largely 
independent of their mean temperature. (Prof. Capper, in Report of 
feteam-Engine Research Com. of I.M.E., 1905.) 

Calculation of Initial Condensation and Leakage. 

Steam not accounted for by indicator c loge r 
Indicated steam ~ d^N ’ 

where r = ratio of expansion, c = 6 to 8 for simple unjacketed engines, 
4 tor jacketed slide-valve engines, 2 to 4 for Corliss engines (jacketed 
a t eted< respectively), and 12 for very poor engines. 

Indicator Diagrams. (Fig. 11.) The figure shows the indicator dia- 
e, am ot a simple condensing engine, ON being the vacuum line or line 



of zero pressure, OS the line of zero volume, and ID the atmospheric line 
of a ^ solute Pressure (0 lbs. gauge). AR is the length of stroke 

and A A the clearance, which is the volume of the valve passages plus the 
volume between the piston at the end of stroke and the cylinder head 
reduced to a percentage of the stroke. (Clearance ranges from 2 to 7% 
of the total volume; when unknown it may be assumed as being 3% for 
well designed engines.) 

The clearance space first fills, pressure rising immediately to A, and 
the piston moves to B, where the steam is cut off, and expansion takes place 
between B and C. If the cut-off is gradual (due to slow closing of the 
steam port), the steam will be “wire-drawn,” and the pressure before cut-off 
will fall along the line AB'. 

The exhaust port opens at C and the pressure drops to D and on the 
return stroke through D to E, wdiere the port is fully open, and remains 
so until F is reached. The exhaust port closing at F, the remaining steam 
is compressed to G (cushioning the stroke), where incoming fresh steam, 
(due to the opening of steam-valve slightly before the commencement 
of the next stroke), rapidly raises the pressure to the starting-point A. 
The space V between the lines FE and ON represents the back-pressure 












64 


HEAT AND THE STEAM ENGINE. 


due to vapor pressure in the* c e 01 ^®^To 3 ^s. S ^der fai^cond? 
perfect vacuum. Back-pre.. BMT is an equilateral hyperbola 

lions. The theoretical expansi°f«V r Tmal) and should be drawn on the 
(assuming the expansion to be iso ^ any po int M on the actual 

diagram or card f ^ r cp n pans° . perpe ndicuTar to SR and intersecting 
expansion cur\e BMC, maw r ’ > and intersecting OK 

it at K. Draw OK, and a so M-L parallel to . theore tical point 


it at K. Draw OK, and. also ML parallel to ^ ^ ~ point 

at L. Draw LB perpendicular to , SR. B by drawin g OK'; 

of cut-off. intersect L'M' (drawn parallel 


Of cut-off. Any other point «[*') mayue (drawn parallel 

then a perpendicular let fal ^ h desired point. Where 

to SR from intersection of OA and ateiv fixed by selecting two 

the clearance is unknown ^ “ a ^ b y,? P dr awing the rectangle BK'M'L' 
points on the expansion line (B M ),■ “g^ction with ON at 0. 

“"raults'shown^by'indicator Cards. (Figl 12.) -C-too eariy Klmi^ 
rifr^too^rlfjeiea^ 

rarircut^H.-cLfed adm, sion ^S'idm.S j feS 
c u t- off;F.vjd oourh haotpress , } ahead . P—indicator inertia; 
g‘-Sng todicator piston; R ,-initial condensation; S.-re-evapora- 

M «e h ore'SS ^ 

atmospheric line, compressed Cta 

the end of compression, when the P S{ of release where the exhaust 

K&SsfiW S5T h 

stroke, the pressure falling as shown by dotted 1 e. ^ ^ Pm L a (2N) 

Calculation of Indicated Horse-Power. I.H.P. = —33^00" ’ w ere 

L-strokl aSd^Vi'r Mofc 

?he SfeCbnateof eaeh on°tl!e dSiamnn'idd’samemd divide by 10, 

fe w. tsms 

obSie the mean height Should there be a loop in the diagram (as 
obta mng tlie meane B cut _ 0 ff) its area should be subtracted from the re¬ 
mainder 1 of the diagram as the pressure indicated by the loop is negative 
Vacuum.— The best vacuum for a reciprocating engine is from -4 to 
*»> "hen rtre i barometer 

ffbeTob"Sna b Je t y e aeu 0 um? each additional inch above 24 in. reducing 

the steam consumption some 4 to o/ 0 . t rr T> = 

Indicated Water Consumption.— Lbs. water per hour per I.H.I . 
107 5\(b + c)w — cW]]-r-Pmi where b = percentage of stroke completed at 
point where the calculation is made (which may be at any point between 
^ * raff orirl rplpaseV c = percentage of clearance to the stroke, w weight 
?n lbf “f cu ft. of steam at the pressure of the point, where the cal¬ 
culation is made; «'i = lbs. in 1 cu. ft. of steam at the final compression 

P I)iatrram Factor. In a theoretical diagram with admission at boiler 
pressure (p) up to the point of cut-off, expansion along a hyperbolic 
curve, release at the end of stroke, exhaust at back-pressure (Pb), and no 

compression, P m = y (1 + loge r)~Pb, where r = ratio of expansion = number 





DIAGRAM FACTOR. 


65 


of volumes the original volume has expanded to, p and Pb being absolute 
pressures. 

The actual P m of an engine may be found by multiplying the right- 
hand member of the above equation by c, the diagram factor. 



Values of c : 0.78 for simple, unjacketed, slide-valve engines. Com¬ 
pound engines,—0.6 to 0-8 for high-speed, unjacketed; 0-7 to 0.85 for 
































66 


HEAT AND THE STEAM ENGINE. 


low-speed, unjacketed; slow-speed, jacketed, 0.85 to 0.9. Corliss, jacketed, 
0.8 to 0.9. Triple-expansion,—high-speed, unjacketed, 0.7; marine engines, 
0.6 to 0 . 66 . 


Hyperbolic Logarithms. 


No. 

Log. 

No. 

Log. 

1 

0 

5.25 

1.6582 

1.25 

.2231 

5.5 

1.7047 

1.5 

. 4055 

5.75 

1.7492 

1.75 

.5596 

6 

1.7918 

2 

.6931 

6.25 

1.8326 

2.25 

.8109 

6.5 

1.8718 

2.5 

.9163 

6.75 

1.9095 

2.75 

1.0116 

7 

1.9459 

3 

1.0986 

7.25 

1.9810 

3.25 

1.1787 

7.5 

2.0149 

3.5 

1.2528 

7.75 

2.0477 

3.75 

1.3218 

8 

2.0794 

4 

1.3863 

8.25 

2.1102 

4.25 

1.4469 

8.5 

2.1401 

4.5 

1.5041 

8.75 

2.1691 

4.75 

1.5581 

9 

2.1972 

5 

1.6094 

9.25 

2.2246 


No. 

Log. 

j No. 

Log. 

9.5 

2.2513 

25 

3.2189 

9.75 

2.2773 

26 

3.2581 

10 

2.3026 

27 

3.2958 

11 

2.3979 

28 

3.3322 

12 

2.4849 

29 

3.3673 

13 

2.5649 

30 

3.4012 

14 

2.6391 

31 

3.434 

15 

2.7081 

32 

3.4657 

16 

2.7726 

33 

3.4965 

17 

2.8332 

34 

3.5263 

18 

2.8904 

35 

3.5553 

19 

2.9444 

36 

3.5835 

20 

2.9957 

37 

3.6109 

21 

3.0445 

38 

3.6376 

22 

3.0911 

39 

3.6636 

23 

24 

3.1355 

3.1781 

40 

3.6889 


Diameter of Cylinder for any given I.H.P. 

d= 144.9V / I.H.P. + V m LN. 


Cylinder Ratios for Multiply Expansion E ngines.—For com¬ 
pound engines (2 cyls.), ratio = V / No. of expansions = 2.8 to 3.5. 

For triple expansion engines: 


Gauge Pressure. 


High Pres- Inter- Low 

sure Cyl. mediate. Pressure. 


130 lbs. 1 2.25 5 

140 “ 1 2.4 5.85 

150 “ 1 2.55 6.9 

160 “ . 1 2.7 7.25 


For quadruple expansion engines: 


Gauge Pressure. 


High Pres- 1st Inter- 
sure Cyl. mediate. 


2d Inter¬ 
mediate. 


160 lbs. 1 2 4 

180 “ 1 2.1 4.2 

200 “ . 1 2.15 4.6 

220 “ 1 2.2 4.8 


Low. 

8 

9 

10 

11 


The most economical point of cut-off in a simple, non-condensing engine 
lies between i and £ of the stroke. 

The Rest Ratio of Expansion. The best number of expansions ( N ) 


in a simple condensing engine is A==^rp(loge 7 - + -^), where r and ri 

are absolute temperatures, V and Vi are vols. in cu. ft. of 1 lb. of steam, L 
and L\ are latent heats. V, r, and L for the beginning and Fi,ri,and L\ 
for the end of the expansion (Willans). 

Combination of Multiple Expansion Diagrams. In order to com¬ 
pare the expansion with any desired theoretical curve, the several dia¬ 
grams of the multiple expansion cylinders must be plotted on the same 
horizontal scale of volumes, clearances being added to the volumes proper. 
Any reference curve R may then be drawn. (Fig. 13). 
































STEAM CONSUMPTION OF ENGINES. 


67 


Steam Consumption of Engines. 

Boiler Pres- Lbs. Steam 


Type. 

Non-Condensing: 

Common Slide-valve. 

Single-valve Automatic, high 

speed. 

Double-valve Automatic, high 

speed. 

Field, with superheat. 

Corliss, Automatic . .. 

Compound 4 4 * high speed.. 

Condensing. 

Corliss, Simple. ; • • 

Compound Automatic, high 

speed. . . : . . . ... • • • • 

Compound Schmidt (superheat) 

‘ * Corliss. 

4 4 Leavitt. 

* ‘ Bollinckx. 

Triple Expansion, Marine and 

Pumping. 

Triple Expansion, Sulzer. 

“ “ , Allis. 

Quadruple Expansion. 

Rice & Sargent Cross-compound.. . 
(Vacuum, 26.8 in., superheated to 
443° F., Cyls., 16.07 in. and 
28.03 in. (r = 3.04)). 


I.H.P. 

sure, Lbs. 

per I.H.P. 


per Sq. In. 

per Hour. 

25 to 100 

80 

33 to 40 

50 44 150 

80 

32 “ 40 

50 “ 150 

80 

30 “ 35 

136 

113 

(18 - 6) „ 

100 to 200 

75 to 90 

22 to 27 (17.5) 

100 ‘ 4 250 

110 “ 120 

25 “ 27 

200 and up 

80 

18 to 20 

200 to 500 

110 to 120 

17 4 4 19 

75 

180 

(10.17) 

400 and up 

110 to 135 

13 to 17 

640 

135 

(12.16) 

300 

90 

(12.19) 

300 to 1,000 

160 to 180 

11.2 to 15 

615 

140 

(11.85) 

575 

120 

(11.68) 


180 to 200 

10 to 12 


420 143.4 (9.56) 


(at throttle) 

Lbs. per 
E.H.P. Hour. 


553 

2,030 

2,030 


150 

150 

150 


13.55 

12.66 

14.7 


Westinghouse - Parsons Turbine, 

(Vacuum, 28 in., superheat, 

100° F., 3,500 r.p.m., full load). . 

Same (superheat, 140° F., 1,500 

r.p.m.).. 

Same (saturated steam, 1,500 

r.p.m.).. 

(A gain of 14% by superheating. 

Consumption at half load is 9% 
greater.). 

The values in parentheses are some of the most economical results ever 

obtained. These figures may be expected r . st _ C ^! )0 ^ S ( J gn i6 jjbs’ 

condensing, 25 lbs.; condensing simple, 18 lbs., compound, io ids., 

tri The e folfowing’are some recent economical results with saturated steam. 
Westinghouse-Parsons Steam Turbine (Dean & Main test), 600 H.P., 
saturated steam at 150 lbs., 28 in. vacuum: 125% load, 13.02 lbs. steam, 
100% load 13.91 lbs.; 75% load, 14.48 lbs.; 41% load, 16.05 lbs.; average, 

85 850 1< HP Rice 1 & b Sargent 1 cSmpmmd Corliss engine, 120 r.p.m.; cylinder 
850 ti l nice <x Uve-steam jackets on cyl. head, live 

steam in reWateT I^OH^ load (150 lbs., 2^.0 in, vacuum 33 expan¬ 
sions) Prof. Jacobus’ test showed a steam tonsumpLon of ^ 

H P hour. The cyl. condensation loss was -2% and tne jacket. 

sumption fo.7% of the total steam used. . , „ , . 

050 HP Van den Kerchove compound engine, with poppet valves, 
126 r o m cvlSder ratio? 1, 2.97: clearances 4%, jackets all over cylinder, 
no reheS'er For 117 H.P. load Prof. Schroter’s test showed a steam 
consumption of 11.08 lbs. per H.P. hour (150 lbs. pressure. 27 6 vacuum 
32 expansions). The cyl. condensation was 23.5/ 0 and tne jacket 

consumption 14% of the total steam. Mat-client & Morlev 

T'ia most economical engine reported is a Vote, iviarcnent oc _> ;e.v 





















68 


HEAT AND THE STEAM ENGINE. 


36 in. Boiler pressure, 114.5 lbs. gauge, temperature of steam, 726° F. 
(=378° superheat). R.p.m. = 100.7; I.H.P. = 145.5. Vacuum 26.5 in. 
Steam per I.H.P. per hour = 8.585 lbs., and at 481 I.H.P., 9.098 lbs. The 
engine is supplied with drop piston valves, and has run successfully for 



Fig. 13. 


over a year, no trouble being experienced with the high temperatures 
employed. (The Engineer , London, June 2, 1905.) 

Governors. Simple Fly-ball or Watt Governor. Let h = vertical 
distance from the point of support of the radius or pendulum arms to the 
plane in which the centers of gravity of the balls or weights revolve at 

q £ °00 1 &7 ft 

any particular speed. Then, h = — ^ inches, and Greater 

, , . N V h 

sensitiveness may be obtained by using the Porter type of governor, which 
has an axial weight w\ in addition to the fly-ball weights (each = u;) of a 

simple governor. In this case h= - !A 35,2Q Q 

Valves. Zeuner’s Diagram, 
the normal slide-valve A should 

A 


in. 


w ) N 2 

When the crank is on the dead-center 
be at half-stroke, 90° in advance of 
the crank and on the point of admit¬ 
ting steam. If the valve has steam 
lap B added to it, the advance 
would necessarily be 90° + steam lap. 
To assist the steam under compres¬ 
sion in cushioning the stroke, steam 
is admitted slightly before the end 
of stroke and at the dead-center the 
valve is then open by an amount 
called the lead, which must be added 
to the advance (90° +steam lap), to 
locate the position of the eccentric. 
, , , Steam and exhaust laps (B and C) 

form an additional width to the valve-face and are for the purpose of effect¬ 
ing an early cut-off of steam or exhaust flow. (Fig. 14.) 



Fig. 14 . 



































2etjner’s valve diagram. G9 


Hie action of a slide-valve is best shown by means of Zeuner’s diagram 
(Fig. 15). On the diameter AF( = 2 Xeccentric throw) draw the circle 
ABFH. In the small diagram (I.) draw the steam-valve circle OF and 
also the exhaust-valve circle OA. With O as a center draw an arc with 
radius 0M( = steam-lap) and also an arc with radius 0/2( = exhaust-lap) 
If the crank is on the dead-center A, the eccentric will be at B, or 90° + 6 
in advance. The intercepts or shaded part MF made by the radius OB 



The diagram may be used to better advantage by turning the valve- 
circles back 90° + 0, as in the main figure. Steam is admitted before the 
end of the previous stroke, the crank position being shown by OK which 
passes through the point N. The angle AOK is the angle of lead. At 
OA the crank is on a dead-center, at OB the steam-port is fully open and 
at OD steam is cut off by the closing of the port. From D to E the steam 
expands in the cylinder. At E the exhaust-port opens, reaching full 
opening at G and closing at J , the steam remaining in cylinder being com¬ 
pressed to K, where fresh steam is admitted for the next stroke. 

OM is the steam-lap, OR the exhaust-lap, and LM is the linear lead 
due to the angular lead AOK. IFF is the wddth of the steam-port and 
the exhaust has full opening from OV to OT. (O is center of circle ABF.) 

























70 


HEAT AND THE STEAM ENGINE. 


By increasing the steam-lap, admission takes place A* 1 ®i.fl'Tnj 

and ceases earlier; expansion occurs earlier and ceases later, exhaust and 

compression are unchanged. .... , i 

By increasing the exhaust-lap admission is unchanged, expansion begiins 
as usual but continues longer, exhaust occurs later and ceases earlie , 
and compression begins earlier and ceases later. . 

By increasing the travel of the valve, admission begins earlier and ceases 
later, expansion occurs later and ceases earlier, exhaust begins and ceases 
later, and compression begins later and ends earlier. h • 

By increasing the angular advance, admission, expansion, etc., all begin 
earlier but their respective periods are unaltered. ,, 

Valve Proportions. Ports should be dimensioned , so f7 

a velocity of about 6,000 ft. per mm. for live steam, and about o,,000 It. 
per min. for exhaust. For a velocity of 6,000 ft. per min., Port area 

(diam. o f cyl.)* X piston speed Lengt i 1 Q f port should be as near diam. 


7,639 

of cyl. as possible, and width 
= tra -- 1 + width of steam-port — width 


area -f- length. Width of exhaust port 

of bridge between ports+ ex- 


^ ia por Corliss cylindrical semi-rotary valves; diam. of admission-valve 
O 9 X width of steam-port; diam. of exhaust-valve = 2.25 X width of exhaust- 
por^ Length =Xm. of cyl. Widths to be obtained from area formula 

^ * 'piston' Speeds in Feet per Minute. Locomotives,' 1,000 to 1,200; 
marine engines, 700; horizontal engines, 400 to 600; pumping-engmes, 
130. Cyl. area-=-port area = 6,000 -5- piston speed m ft. per min. 

Flow of Steam. Lbs. per min.=0.85ap wnen discnargmg into the 
atmosphere. When flowing from one press ure to a nother which is d lbs. 

less and p — d> .58p, lbs, per min. = 1.9 aW{p-d)d. Jc = 0.93 for a short 
nozzie and 0.63 for an orifice in a thin plate (p — absolute pressure). Also, 

velocity in ft. per sec. =3.5953^ when A-height in feet of a column of 
steam of the given absolute initial pressure and of uniform density, whose 
weight is equal to the pressure on th e un it ot base. 


Flow of Steam in Pipes. 


L 


where L and D are the length 


and diameter of the pipe in feet and H is the height in feet of a column 
of steam at entrance pressure which would produce a pressure equal to 
the difference between the pressu res at the ends of the pipe. 

Q, in cu. ft. per min. = 4.72334^-y— t where <i = diam. of pipe in inches 


IF, in lbs. flowing per min. = 87 


/ w(Pi~ P-2)d 5 

V ^+ 3 - r ) 


where w 


= lbs. per cu. fh 


of steam at initial pressure, Pi, and p 2 =pressure at the end of pipe. 

The Setting of Corliss Valves. There are three marks on the hut- 
of the wrist-plate which indicate the extremes of throw and the centra* 
position accordingly as they coincide with another mark on the stand. 
Fix the wrist-plate in the central position, unhooking the rod connecting 
to the eccentric, liemove the back bonnets of the valves, and marks 
will be found on the valves and valve-chambers which indicate respectively 
the working edges of the valves and ports. By means of the adjustable 
rods which connect the valve-arms to the wrist-plate set the steam-valves 
so that they will have a lap of I to £ in. (the former for a 10-m. cyl., and 
the latter for a 35-in. cyl.,—intermediate sizes in proportion). 

Similarly, set the exhaust-valves with tV to £ in. lap for non-condensing, 
and with ~£ to £ in. lap for condensing engines. 

Adjust the dash-pot rods by turning the wrist-plate to the extremes 
of travel and regulate their lengths so that when they are down as tar 
as they will go the steel blocks on the valve-arms will barely clear the 
shoulders on the hooks. (If the rods are too long they will be bent, if 
too short the hooks will not engage and the valves will not open.) 

Hook the connecting-rod to the wrist-plate, loosen the eccentric, turn 
it over and adjust the eccentric-rods so that the wrist-plate will have correct 











INERTIA DIAGRAMS. 


71 


extremes of travel, as shown by the marks on hub. Place the engine on 
either dead-center, turn the eccentric enough more than'one-fourth of a 
revolution in advance of the crank (in the direction of rotation) to show 
an opening of the steam-valve (at the piston end of cylinder) of gC to £ in., 
according to the speed, this being the lead. The higher the speed the 
more the lead required. Set tlie eccentric, turn to tne other dead-center 
and obtain the same lead by adjusting the length of the rod connecting 
to wrist-plate. To adjust the regulator connections to the cut-off cams, 
turn the wrist-plate to one extreme of travel and adjust the rod connecting 
to the opposite cam so that the cam will clear the steel in the tail of hook 
by gb in. Turn to the other extreme of travel and adjust the 
other cam. To equalize the cut-off, block up the regulator about li in., 
which is its average position when running. Turn the engine slowly and 
note the positions of cross-head when the cut-off cams trip and the valves 
close. These positions should be at equal distances from the respective 
extremes of travel of the cross-head, and the rods should be adjusted 
until they are. Indicator cards should then be taken and such readjust¬ 
ments made as are required for the equalization of the diagrams. 

To Place an Engine on a Dead-center. Locate by a mark on the 
guides the position of a mark on the cross-head when it is at any point 
near the end of the outward stroke. Denote this position on the fly¬ 
wheel rim by a mark which coincides with a fixed reference pointer. Turn 
the engine beyond the dead-center and on the return stroke until the 
mark on the cross-head coincides with that on the guides. Note this 
position on fly-wheel by making a mark at the reference pointer. Find 
the point midway between the two marks on the fly-wheel rim and turn 
the engine until this mid point coincides with reference pointer and the 
engine will be on a dead-center. To avoid the errors which might arise 
from looseness of bearings, the engine should be turned a little beyond 
the original position on the return stroke and the motion then reversed 
up to the original position so that the same brasses will press on the crank- 
pin in both observations. 

Acceleration, Inertia, and Crank-effort Diagrams. The effect of 
the reciprocating parts of an engine is shown in Fig. 16. A vertical 
engine is chosen for illustration as both the inertia force and the dead 
weight of the moving mass are present, the effect of the latter being absent 
in a horizontal engine. Draw the crank-circle JKLM with radius 0 4 = 
21 in. and the connecting-rod 3 4 = 90 in. Draw the polar velocity curves 
KU and MU and also the velocity curve AXB. These curves are con¬ 
structed as follows- In (II), if W moves uniformly, AW represents the 
crank velocity. Project the connecting-rod PW to C and AC will then 
be the corresponding piston velocity of the point P. Revolve AC to 
AE on the line A W and E will be a point in the polar velocity curve. Trans¬ 
fer AC to PF and F will be a point in the velocity curve JKH. The 
remaining points of each curve are similarly determined. The crank 0 4 
makes 88 rev. per min., and the crank-pin consequently has a velocity 
of 16.1 ft. per sec. and OK (=ordinate X) should be divided into 16.1 parts 
to serve as a scale of measurement. The acceleration curve, QTR must 
then be drawn by the method shown in (III). Let AEB (III) be the 
velocity curve. Draw a tangent at any point E, a normal, ED and let 
fall a perpendicular EC to AB. Set off CF = CD by revolving CD through 
90° and F will be a point in the acceleration curve GKII. QT and TR 
show respectively the increase and decrease of velocity for the downward 
stroke and RT and TQ the acceleration and retardation for the up stroke. 

The force moving the reciprocating parts around the dead-centers J 


and 


wv* 


L = ^~. The 
oR 

16.1X16.1 1/IQ 

■-—— ; —- =148 ft. per sec. 

1.75 


wf . V* 

inertia force, =—.whence, /, the acceleration = -=r 
g R 


AQ, therefore, should be divided into 148 

parts for a scale of acceleration in ft. per sec. The moving parts of the 

wf 

engine weigh 8,030 lbs. and the inertia force at any moment, F = — = 


o non 

Xacceleration, or, at AQ( = 148 ft. per sec.), F 

32.16 


36,911 lbs. Draw 


NSP below QTR , each ordinate of distance between the two curves being 
equal to QN, which is 8,030 lbs. by scale where AQ = 36,911 lbs. NSP 



72 


HEAT AND THE STEAM ENGINE. 


is the curve of inertia pressure. The pressure per sq. in. on piston at 
AQ = 36,911 -s- 491( = area of piston in sq. m.) = 75.2 lbs. Draw the indicate 
cards to this scale, viz.: EQXHB for the top of piston and FPGA tor 



the bottom. When QXHB is being drawn by the indicator on the top 
side of piston, AFR is being drawn on the bottom side, and, deducting 
the ordinates at F from those at H, the net effective pressure will be repre¬ 
sented by the solid line WR. Similarly, by deducting E ordinates from 















INERTIA DIAGRAMS. 


73 


G the curve of net pressure is shown along VN The actual total pres¬ 
sure transmitted to the crank-pin during the first half of the stroke will 
t>e less than that shown on the indicator diagram by the amount required 
to set the reciprocating masses in motion, and during the latter half of 
the stroke the indicated pressure will be, increased by the backward pull 
I * e jf r c *fd to absorb the inertia. The top card accordingly loses the area 

r *i * gau ? s D 'A,^Vct^ re8ulting P^ssure areas then being NIXWPSN 
tor the top and PZ l N BP for the bottom, or, erecting the resulting ordinates 
ep 'he base AB, the top and bottom areas are respectively AbdBA and 
BefAB. lo equalize these areas it will be seen that the cut-off on the 
bottom diagram is considerably later than that on the top diagram, on 
account of the dead weight which has to be supported. Only the recipro¬ 
cating parts cause inertia force. The crank end of the connecting-rod is 
a rotating part, and it is customary to assume \ of the weight of the rod 
as reciprocating. The revolving parts are balanced by opposing weights 
on the crank-shaft. When the crank is on either dead-center all the 
pressure is received on the bearings, while at mid-stroke the pressu r e is 
exerted tangentially wdth no pressure on the bearings excepting that 
due to weight. At all other points the pressure is partly tangential and 
partly normal. The tangential pressure at any point is proportionally 
represented by the corresponding radius vector of the curve KZJ If JO 
is then divided into tenths the length of each radius vector in terms of 
these divisions will represent its virtual crank-arm in relation to the pres¬ 
sures transmitted along ABO. Multiply each net pressure ordinate along 
AB by its virtual crank-arm and set off the resulting tangential crank 
pressures radially, with the crank-circle JKLM as a base line and the 
curves of crank-effort, JghjL and LklmJ will be obtained. These curves 
may be set out on a straight base by stepping JK out on CO, and KL 
on OD and then transferring the radial ordinates to vertical positions 
along the line CD when the curves CnD and DpC result. In locomotives 
two cranks at right angles are employed and in marine engines three cranks, 
120° apart. A combination diagram may be made by superposing the 
diagrams of the individual cranks and adding the radial ordinates. (The 
foregoing discussion is taken from Lineham’s Text-Book of Mech. Eng.) 

Calculation of Fly-Wheels. On the base line EH (Fig. 17) lay out a 
series of crank-effort diagrams, making EAF and FCG equal to DpC 
and CnD of Fig. 16. EG= 1 rev. = 34^ = 11 ft. The mean ordinates of 
EAF and FCD are 29,500 lbs. and 25,000 lbs. respectively and one-half 
their sum, or 27,250 lbs., is the mean effort for the continuous diagram. 
Draw JK at this pressure above EH. The areas A, C, etc., above the 



line JK show surplus work, while B, D, etc., below the line show deficits. 
The fly-wheel must absorb the work of A , C, etc., and give it out again 
at B, D, etc., thus tending to equalize the crank-effort. The mean pres¬ 
sures and distances are measured at A, B, C, and D and are shown by 
the work rectangles, and A +C = B + D = 88,700 ft.-lbs. The greatest 
rectangle is D, =49,560 ft.-lbs., which is the amount of energy the fly¬ 
wheel must be able to deliver and thereby decrease its velocity. The 
heavier the wheel the smaller will be its fluctuation of velocity. Let r = 

• . V 

mean velocity in ft. per sec. and let the total fluctuation of velocity = -y-, 

k 

where k varies from 20 to 300, according to the steadiness required. Let 
Vi and V2 be the maximum and minimum velocities at the mean radius, 



















74 


HEAT AND THE STEAM ENGINE. 


w(Vi i — V‘2 2 ) __ jp 

E = the energy area (in this case 49,560 ft.-lbs.). Tien 


where w = weight of wheel in lbs. Now, 
v = 2nRN -5- 60, where R = radius of gyration «J 9 ^ eel 111 feet ‘ 
and reducing, weight of wheel in lbs. w 


— + 1>2 — 2v, and 

Substituting 


2,932Jfc Va , uesofi; (1.. 




- per¬ 


centage of fluctuation from 5 . for pumping and shear- 

with the f^he hub h aml arms are of considerable weight, assume a section 
section If the ^ubana ai equal ght and trea t 

in both*feet and inches. 

w = Cd~s^ w here d, s, and D are diam. of cyl. in in., stroke in in., and 

sr SbSd | 

himfrom some 160 engines (from 12 American builders) ranging from ‘20 
. i-n H P Those of J. B. Stanwood are the conclusions of an extended 
t0 there of Wm Kent are the best probable mean expressions 

Tf wrJumber of formulas considered and discussed by . him in The 
of a_large number Book . The following notation is employed; 

^anica 1 Enemeer^s Focket «O gtrok ^ * f pi d , =diam. of 

a area P ’ r cylinder studs, < = thickness, Z]=length of con- 
fly-whee , ^ ^.11 in inch measure. JV = r.p.m., p = max. 

nectmg-rod >■ in y = piston velocity in ft. per min., H.P. 

|n e d m iHP S =?ated and indicated horse-power, respectively. (See also 
related matter in Strength of Materials, ante.) 


Cylinder: 

Thickness of walls, 

“ “ flanges, 

“ “ heads, 

Studs, No. of (6), 

“ diam., 

Length of piston, 

44 4 4 “ 

Piston-rod diam.: 

High speed, 

Low “ 
Connecting-rods: 

High speed, rectan- 
g u 1 a r section, 

thickness, t = 
Mean height = 


section, 
diam. = 


mean 


Barr. 

Kent. 

Stanwood. 

0.05d + 0.5 in. 0.0004dp + 0.3 in. 

1.2 X above 

“ “ 0.00036dp + 0.31 in. 

0.7d 0.0002 d 2 p + s 2 

0.025d + 0.5 in.0.01414^p-i-6 

0.46d (h.s.) 1 A/— 

0.32 d (l.s.) > V ld 


0.145V75 ) 
0.11 V/d \ 

O.QlWvld 

0.14d to 0.17d 

0.05 7^hd 

2.7 1 

0.01d' v/ p*+0.6 in. 
(Crank end, 2.25Z, 
cross-head end, 
1.50 


0.092Vzd 

0.021 d^p 








STEAM-ENGINE PROPORTIONS. 


75 


Cross-head pins: 

( L = length, Z) = diam.) 


Barr. 


High speed, 


Low 


LD = 0.08a; =1.25 


Crank-pins: 

(L = length, D = diam.) 


LD^O.Ola; ^ = 1.3 


High speed, 


LD= 0.24a; L 


0.3H.P. 

/ 


+ 2.5 in. 


Low * * 

Crank-shafts, Main Journals: 


r r* r> r>n T 0.6H.P. , „ . 
LD = 0.09a; L— ---1-2 in. 

L 


Stanwood. 

| L = 0.25d to 0.3d 
j Z> = 0.18dto0.2d 

L = 0.25d to0.3d 
D = 0.22d to 0.27d 


Highspeed, I 

LD - 0.46a; D - 7.3l^ H ^-; L 

= 2.2 Dj 

L = 0.85d to d 

Low ' ‘ ( 

LZ) = 0.56a; D = 6.8|/^^; L 

= l.w) 

D — 0A2d to 0.5d 

Steam-ports, area: 



Slide-valve, 



0.08a to 0.09a 
0 .1a to 0.12a 

High speed, 

a7v 5,500 


Corliss, 

a7-r 6,800 


0.07a to 0.08a 

Exhaust-ports, 
Slide-valve, 
High speed, 

area: 


0.15a to 0.2a 
0.18a to 0.22a 

aV = 5,500 


Corliss, 

aV = 5,500 


0 .10a to 0.12a 

Steam pipes, area: 



Slide-valve, 
High speed, 

aV = 6,500 

diam.= 

0.25d + 0.5in. 
0.33d 

Corliss, 

a F = 6,000 


0.3d 

Exhaust-pipes, 

area: 



Slide-valve, 
High speed, 

aV = 4,400 

diam.= 

0.33d 

0.375d 

Corliss, 

a V + 3,800 


0.33d to 0.37d 


Slide-valve, 
High speed, 
Corliss, 

Weight of engine: 

Slide-valve, 
High speed, 
Corliss, 


i ,200 ,ood ,666 !ddo d^N 3 


115 ibs. per I.H.P. 
175 “ “ 


33 

25 to 33 
80 to 120 

lbs. per H.P. 
125 to 135 
90 to 120 
220 to 250 


Piston speed in ft. per min. = 600; weight of reciprocating parts in lbs., 
for high-speed engines = 1,860, 000d 2 + lN 2 ; square feet of belt surface per 
I.H.P. per min. = 55 (high speed) and 35 (low speed) (Barr). 

Clearance space: Corliss, 0.02/ to 0.04/; high speed, double valve, 0.03/ 
to 0.05/; high speed, single valve, 0.08/ to 0.15/; slide-valve, 0.66/ to 
0.08/. Pressures on wearing surfaces in lbs. (L = length, D = diam., both 
in in.): Main bearings, 140 LD to 160 LD; crank-pins, 1,000LZ) to 1,260 LD; 
cross-head pins, 1,200LD to 1,600LD (Stanwood). 

Pressure on thrust-bearings = 35 to 40 lbs. per sq. in. of area (Fowler). 

Receiver volume for compound engine. If the cylinders are tandem, 
the connecting steam passages will be sufficient. If the cranks are at 90°, 
the volume of receiver should be at least as great as that of the low-pres¬ 
sure cylinder. 


















76 


HEAT AND THE STEAM ENGINE. 


TEMPERATURE-ENTROPY, DIAGRAMS. 

In an indicator diagram the co-ordinates am pressure and volume and 
the area represents work do ^ e . t he ’vertical ordinates are absolute 

euerey 1,1 

Un isothermals° S on' 1 tlns 1 ^diagrain ^^ a ticl*are*verfilmi^traight 9 line^—inhere 
perature being constant, and adiaba - ,urine a change of temperature, 

being no change in the Quantity of heat dunng a cna g at Tl = 

Application to Carnot Cycle (hi g. heat rejeCted t T2 = 

area H 2 ] AB and CD being isothermals 
and BC and AD being adiabatics. 
Work done = H\ — H 2 , and efficiency 

Construction of Diagram for 
Water and Steam. The diagram is 
drawn to represent the changes ot 
1 lb. of working substance and an 
arbitrary zero point is ch o sen t « 
work from (i.e., 32 r, or ‘vat 

absolute). The entropy of water, 
then, at 492° =0. At any other 



tnen, at =o. —* 

absolute temperature, t, the en tropy 
_. 10 of water, <fnv = log* t — loge 49- 

Fig. lo. loge t — 6.198. 

The additional entropy due to the conversion of water into steam is 
































TEMPERATURE-ENTROPY DIAGRAMS. 


77 




divided by the corresponding absolute temperature, or = ^ . The 
following table gives the s 


Entropy per Eb. Weight. 


t 

T 

Water from 
32° F. (* w ). 

Steam (<£ s ). 

Steam and 

W ater + 

32 

492 

0.0000 

2.2189 

2.2189 

50 

510 

.0359 

2.1163 

2.1522 

100 

560 

.1296 

1.8649 

1.9945 

150 

610 

.2154 

1.6547 

1.8701 

200 

660 

. 2949 

1.476 

1.7709 

250 

710 

.3690 

1.322 

1.691 

300 

760 

.4386 

1.188 

1.6266 

350 

810 

. 5042 

1.0698 

1.574 

400 

860 

. 5665 

0.9649 

1.5314 


The results in this table are plotted in Fig. 19, ON being the water line 
or the plotting of the values of <j>w , and MP the dry-steam line, or + 

If 1 lb. of water is raised from 32° F. to tj, the heat units required will be 
represented by the area Ot\A. The heat then required to convert the 
water into steam will be the area z\BCAz\ The entropy of the water 
will be OA as measured by the scale, that of the latent heat by AC, and 
the entropy of the steam and water by OC(=OA +AC). 

From steam-tables it is found that 1 lb. of dry saturated steam at 334° F. 
(794° ab.) occupies 4 cu. ft. If the isothermal at this temperature be 
divided into four equal parts, each part will represent 1 cubic foot. Also 
qh may be divided into eight parts, each representing 1 cu. ft. (1 lb. = 8 cu. 
ft. at 284° F.). Other isothermals may be similarly divided, and if all 
of the points for say 1 cu. ft are connected, the resulting curve will be 
a curve of constant volume (for 1 cu. ft.). 

If 1 lb. of water at 334° F. be supplied with heat sufficient to evaporate 
one-quarter of itself, the distance dK will represent the portion of the total 



heat de required for the whole lb. The dryness of the steam (| of it being 
evaporated) will then be 0.25, and it may be stated that. The dryness 
is represented in the entropy diagram by the fraction (hor. dist. of point 
from w^ater line)n-(hor dist. bet. steam and water lines ) = dK-r-de in the 
instance under consideration. 






























7S 


HEAT AND THE STEAM ENGINE. 


If the steam is superheated to t. before enterinl; the eylinder. the axjdU 
tional entropy, CL, is obtained from the formula. Entropy, 

U To' iTravvVhe Entropy Diagram from the Data in an Indicator 

Diagram. —Fig. 20 is tne indicator diagram of an engine having 

ing dIS Initial pressure, 105 lbs., back-pressure, 17 lbs. (both absolute). 





Fig. 21.. 

r p m = 90• cylinder, 14X36; m.e.p. = 34.56 lbs.; I.H.P. = 87.06; area 
of P cvl. = 153.94 sq. in.; volume of cyl. = 3.207 cu. ft.; ^ clearance 

(3.448%) = 0.11058 cu. ft.; lbs. steam used per hour-2,133.5 ( 24,5 

lbs per I.H.P. hr.); lbs. of entering steam per stroke-0.19io4/. 

The compression steam is generally assumed to be dry, and, at point 17 
(where vol =0.16587 cu. ft and pressure = 60 ' lb.E its‘ weight_ will be- 
0 16587X0.14236(or the weight of 1 cu. ft. at 60lbs.) — 0.023613 lb. . . 4otal 
steam in cyl. =0.197547+ 0.023613 = 0.22116 lb. and the vol of 1 lb. 
of steam similar to that in the cylinder, x = actual vol. m cyl. . 0.2-116. 
The pressures and values of * for the various points of Fig. 20 may now 
be plotted on Fig 21. For example, the pressure at point 7 on the 
indicator diagram is 40 lbs, (absolute). lhe content3 ct cyl. at this 






























































1 


TEMPERATURE-ENTROPY DIAGRAMS. 79 


point are 1.7694 eu. ft.., wliich, divided by 0.22116, gives the volume r. 
of 1 lb or 8 cu. ft. and point 7 on the entropy diagram is thus 
located by the intersection of the constant- 
volume curve 8 and the horizontal line of 
temperature 267° F. (727° abs.), which corre¬ 
sponds to a pressure of 40 lbs. absolute. 

Dosses. The entropy diagram just con¬ 
sidered may be compared with that of the 
Rankine cycle for an ideal engine where the 
expansion is adiabatic down to back-pressure 
and where there is no compression. This 
latter diagram is the area A BCD A, BC 
being drawn at 108 lbs. (assuming a drop 
of 3 lbs. from the separator to cylinder). 

The loss BE4GCB is that due to wire¬ 
drawing during the entrance of the steam; 
loss 4GH64 occurs during expansion and is 
due to condensation, leakage, etc.; loss 
JK12J is due to incomplete expansion; 
loss 13A..ET 16 13 is due to clearance, com¬ 
pression, etc. All areas represent heat-units 
according to scale. The area 4LMN4 
represents additional liquefaction loss after 
cut-off, and 7NKJ7 the gain due to re¬ 
evaporation. Fig. 21 shows only the work¬ 
ing part of diagram, the full diagram on a 
smaller scale being shown by Fig. 21a. 

Entropy Diagrams Applied to Inter¬ 
nal Combustion Engines. <$> = U-±z\ 
d<f)=dH+- t. dH = kvdz + (AP h- J)dV , and 
(4P-rj r ) = (L- kv)z-i- V, or, combining these 
equations, dH -j-r = d<f> = (kvdz-r-z) + (/c p — kv)d V 
-r- V, which is the general equation for change 
of entropy. (A = numerical constant, 

J = Joule’s equivalent = 778, P = lbs. pressure 



Fig. 21a. 


per sq.ft.) Integrating between limits, fa — <f > 2 = kv\ogetzi+z 2 ) when the 
volume is constant, and fa — fa — k p loge (zi~hz 2 ) when the pressure is con¬ 
stant. 

When P and V vary according to the law PV X = constant, considering 
that PV = Rz, letting kp + kv — y, substituting in the general equation and 


• cc — y T] 

reducing, <f>i — fa = kv ——loge —, or, the change in entropy when PF* = 

1 T2 

constant. 

In adiabatic expansion y^x, hence fa — <£2 = 0 . „ r 

In the theoretical gas-engine diagram (Fig. 22, I.) Pb = PaVa -r-Vb , 
and zb = PbVb-i-(Kp — Kv), where Vb — specific volume of explosive mixture 
at b, K P and ive = specific heats of mixt ure in ft .-lbs. ( =A> and kv multiplied 
by 778, or the equivalent of 1 heat-unit in ft.-lbs. In the following calcu¬ 
lations the old value,—772,—has been employed). If z a is known, t6 = 
Ta(r)r —*, where r=V a ^-Vb and y = kp -s- kv. z c = zbPc-^Pb. 

The increase of entropy during the explosion is represented by the 
logarithmic curve be (II, Fig. 22) and increase of entropy from b to c — 
fa — <f>b = kv loge (z c -r-zb). Adiabatic expansion is shown by the vertical 
line cd, there being no change in the amount of entropy. zd-PdVd-i- 
( K v - Kv) and Pd = P. VJ h- VdJ = P c VbT = VK 

From d to a (exhaust at const, vol.), fal — <j>„=kv loge (zd+za) which 
is negative. The exhaust and suction strokes do not enter into considera¬ 
tion, the temperature being assumed as constant. 

The diagram is completed by drawing OX at the absolute zero of tem¬ 
perature, when the work done per cycle = area abed ; heat received per 
cycle = area ObcX ; thermal efficiency = abed -5- ObcX , heat rejected into 
exhaust = area OadX. 

Since ( <f>c — <j>b) = (<f>d — <f)a ) and be is governed by the same law as ad, the 
ratio of the two temperatures is constant and dependent only on the amount 
of compression, a high ratio resulting in a correspondingly increased 
efficiency. 

The indicator card of a Crossley Otto engine tested by Prof. Capper 










80 


HEAT AND THE STEAM ENGINE. 


is shown in III, Fig. 22, the data for and a more complete analysis of which 
may be found in Golding’s “Theta Phi Diagrams.” 

Cylinder, 8.5 in. diam. by 18 in. stroke, vol. =0.591 cu. ft., clearance 
vol. =0.2467 cu. ft., total vol. =0.8377 cu. ft. R.p.m. = 162.5, explosions 
per min. = 71.2, net I.H.P. = 13.32. Gas used per hour = 279.75 cu. ft., 
gas per explosion = 0.06544 cu. ft. at 518° F. and 14.8 lbs. pressure, abso¬ 




lute ( = 0.0822 cu. ft. at temperature and pressure at a, or 605° and 13.8 lbs.) 
Pressures in lbs. per sq. in. at a, b, c, d and e = 13.8, 67.8, 240, 240 and 
48.71, respectively. Volumes in cu. ft. at same points = 0.8377, 0.2467, 
0.2467, 0.2617 and 0.8377, respectively. Since p a V a x = PbVb x , from the 
above values of p and V, x = 1.3707 for the ideal expansion curve = 1.3022 
for the compression, curve (both dotted). The location of e is found by 


















TEMPERATURE-ENTROPY DIAGRAMS. 


81 


prodiicing the actual expansion curve until it intersects the vertical ae. 
/* le (London) used had the following percentages by weight: 

CH 4 , 4 2 /9; C 2 ti 4 and C 4 ri s , 18.21; H, 8.69; CO, 18.33; N, 7.14; (_(> 2 
and O, 4.84 1 cu. tt. = 0.0329 lb. &c = 0.5279, A- P = 0.6961. The prod¬ 

ucts of combust on or exhaust gases had the following composition (by 
weight): C0 2 , 10.17; O, 6.7; N, 83.18. Aw = 0.1716, k P = 0.2385, 1 cu. ft.= 
O.OoJ lb. 


The clearance (filled with exhaust gases) held 0.2467X0.082 = 0.02023 lb. 
at and 141 lbs -’ or > [(0 02023 X4„2X 14.8) = (605 X 14.7)] = 0.01656 lb. 
at 605 and 14.8 lbs. pressure at the beginning of suction stroke. The 
gas (0.06544 cu. ft.) having a specific volume of 34.87 cu. ft. per lb. at 
atmospheric pressure and temperature weighed 0.001877 lb. (Vol. at 
605 and 14.8 lb. = 0.0822 cu. ft.) Air per explosion = 0.8377 — 
(0.2467+ 0.0822) = 0.5088 cu. ft., which, at 605° and 13.8 lbs. pressure at 
a weighed 0.03131 lb. (16.25 cu. ft. per lb.). Total weight of mixture = 
0.049747 lb. 

Specific heats of mixture Kv = 141.43 ft.-lbs., A p = 199.09 ft.-lbs., 
A P -Aa = 57.66 ft.-lbs., * P = 0.25788, A: w = 0.1832, r = 1.4077. From these 
values and the previously given temperature equations, rft = 840°F. 
(absolute), r c = 2,973°, rrf = 3,154°, re = 2,048°, and t„ = 580°. (This is 25° 
lower than the value assumed, 605°, but the difference need not be con¬ 
sidered.) 

Taking entropy at 6 as zero, the entropy at c = <f> c — <f>b = kv loge (T C +rb) = 
0.23158. <f>d — <j) C = kp loge (t<*h-t c ) =0.25788Xloge(3,154 2,973) = 0.01524. 


<f>e — >pd = ki~~ log e{zd+xe) = 0.1832[(1.3707-1.4077)0.3707]loge(3,154 -h 

X 1 


2,048)—0.00709. <f> a — <f>e = kv loge (re-j-r a ) =—0.23112. <f>b — (f> a —kv ^—£ 

loge (rb-t-Ta) = —0.02369. Positive entropy, b to e = 0.23158 + 0.01524 + 
0.00709 = 0.25472. Negative entropy, e to 6 = 0.23112 + 0.02369 = 0.25481. 
The two sums should exactly balance, the slight difference being due 
to insufficiently extended calculations. 

The diagram for the ideal cycle is represented by abcdea (IV, Fig. 22), 
whose area = 171.875 B.T.U.. or the work performed by 1 lb. of the mix¬ 
ture. The work per explosion (i.e., of 0.049747 lb.) = 8.55 B.T.U. = 6,600 
ft.-lbs. The actual cycle is now to be considered. The curves be and cd 
in the entropy diagram are correct, but during expansion the actual curve 
of pressures differs considerably from the ideal or dotted curve, and it is 
therefore necessary to select several points on the actual curve and calculate 
the temperature and entropy at each. These values are given in the fol¬ 
lowing table: 


Point on 
Diagram. 

P, 

Lbs. per 
Sq. In. 

V, 

in Cu. Ft. 

T, 

in Degs. F. 

X. 

Entropy ( <f> ). 

d 

g 

240 

170 

.2617 

.335 

3,154 

2,858 

1.3965 

1.4668 

1.4798 

1.2995 
1.3526 

.24682 

.24734 

h 

134 

.394 

2,650 

.24559 

i 

k 

109 

80.5 

.453 

.572 

2,478 

2,312 

.24374 

.24837 

l 

62.5 

.6897 

2,164 

.25027 

m 

53.8 

.749 

2,023 


.24404 

n 

38 

.808 

1,541 


.200 

o 

24 

.8377 

1,009 


.1217 


At m, just after release, p = 53.8 lb.; the pressure at / on ideal curve 
(vertically above m ,—at same vol.) = 56.79 lb.; rm = PmVm-^(K p — Kv)X 
0.049747 = (53.8X 144) X0.749 = (57.66 X 0.049747) = 2,023°; r/=2,135°. 

The drop of entropy from 2,135° to 2,023° = 0.1832 loge (2,135 -h 2,023) = 
0.00991, which must be subtracted from the entropy at /. 

x — Y 

The entropy at / in excess of that at d^kv—^rloge^d-s-zf) = 0.00713, 

X 1- 

consequently the entropy at m=eritropy at d + additional entropy to / 
— drop in entropy from / to m = 0.24682 + 0.00713 —0.00991 = 0.24404. 
Values for points n and o are similarly obtained, the results being included 
in above table. , . . 






82 


HEAT AND THE STEAM ENGINE. 


The heat transformed into work = area abcdjloa. This, however, does not 
represent the total heat generated during the explosion. The total avail¬ 
able heat of each explosion =36.04 B.T.U. (or that of 0.001877 lb. of 
gas, whose calorific value is 19,200 B.T.U. per lb.). To represent this on 
the diagram, produce be to p so that the area. b\bpp\ = 36.04-f 0.049747 = 
724.5 B.T.U. per lb. of mixture. r p =r b + z r (r r =the rise in temperature 
from b due to complete combustion). r r = 724.5 -t-fcv = 3,955° and zp = 
3,955 + 840 = 4,795°. Net heat transformed into work = abcdjlo = 8.2 
B.T.U. per explosion, or 22.75% of the total available heat. Heat given 
to cylinder walls during compression stroke = a^abbi = 0.77 B.T.U Heat 
given to exhaust = a\aomU x = 13.63 B.T.U The remainder ( l\ljdcpp\ = 
13.44 B.T.U.) is transmitted through the cylinder walls, and the total 
heat passing through walls = 13.44 + 0.77 = 14.21 B.T.U = heat given to 
jacket water plus that radiated from the exterior surface of cylinder 
head and piston. 

In an ideal engine (i.e., one with a non-conducting cylinder, complete 
combustion, exhaust at constant volume, adiabatic expansion and com¬ 
pression) the work per explosion = area rbpq, and the maximum possible 
w r ork = 100 (zb — z„)-^-zb ner cent of the total heat evolved, = 100(840 — 580) -5- 
840 = 30.95% of the 36.04 B.T.U. = 11.154 B.T.U. per explosion. The 
net work actually obtained = 8.2 B.T.U. = 73.5% of the maximum. The 
same general method is employed for oil engines, temperatures being 
calculated from PV-=Rz, etc. In a Diesel engine where oil is sprayed 
into the cylinder under air pressure for 5 to 10% of the combustion stroke, 
k P = 0.264 (mean value) and if y is taken at 1.408, /cv = 0.1875. 


STEAM TURBINES. 

Turbines are machines in which a rotary motion is obtained by means 
of the gradual change of the momentum of a fluid. 

In steam turbines the energy given out by steam during its expansion 
from admission to exhaust pressure is transformed into mechanical work, 
either by means of pressu e or of the velocity of the steam while expanding. 

The De Laval turbine is one of pure impact and consists of a w r heel 
carrying a row of radially attached vanes or buckets. The steam is 
delivered to these vanes from stationary nozzles, in which it is fully expanded 
(thus attaining the highest practicable velocity) and after passing the 
vanes is exhausted either into the atmosphere or into a condenser. The 
nozzles a-e inclined to the plane of the wheel at an angle of 20°; the inlet 
and outlet angles of the A r anes range from 32° to 36° according to the 
size of the turbine. The best peripheral velocity is about+7% of the steam 
velocity. Economical reasons restrict it to about 1,400 ft. per sec. for 
large wheels and 500 ft.. per sec. for small ones. R.p.m. of wheels range 
from 10,000 to 30,000, and are reduced to 0.1 these values by helical gears. 

In the Parsons turbine a drum with rows of radial vanes revolves in a 
stationary case. Between each row of moving vanes there is a ring of 
vanes fixed to the case which deflects the direction of the steam flow to the 
next rotating row of vanes. The diameters of drum and casing increase 
in steps from inlet to exhaust end, the steam flowing through the vanes 
in the annular space between the drum and case. The expansion is prac- 
tically adiabatic 

The Bateau multicellular turbine in effect consists of a number of wheels 
of tlie De Laval type mounted side by side on the same shaft, each wheel 
rotating in a compartment of its own and the exhaust of each wheel being 
led through nozzles or openings in the partition w'alls to the next succeed¬ 
ing wheel. Step-by-step expansion and moderate speeds are thereby 
obtained. 

In the Curtis turbine the nozzles deliver steam at a velocity of about 
2,000 ft. per sec. and this velocity is absorbed by a series of moving vane 
wheels on a vertical shaft with alternating fixed rings of stationary guide 
blades, similar to Parsons’ arrangement. 

When the initial velocity has been absorbed the steam is again expanded 
through another set of nozzles to a further series of wdieels, and so on. 
By this comnounding the peripheral speed is kept dowm around 400 ft. 
per sec. In the following table the pressures are gauge pressures. 




STEAM TURBINES 


83 


Steam Turbine Data. 


Make. 


Parsons. 

4 

4 4 

De Laval. 

4 t 
4 4 
I 4 
< 4 . 

Curtis. 

Rateau 


Steam 

Size. Vacuum. Pres- 




in. 

sure. 

lb. 

400 

K.W. 

25 

125 

1,250 

4 4 

25 

150 

1,250 

4 4 

28 

150 

30 

H.P 


100 

30 

4 4 


50 

30 

4 4 

25.5 

125 

300 

4 4 

27 

200 

300 

i 

27 

200 

2,000 

K.W 

28.8 

160 

500 

H P 

(1.33 jg) 

a 

62 


o nos. steam per Jri 

R.P.M S«Pe r - 0 .5 ^ „ : , 

heat. Road. M Load. 

° F. 


3,300 

0 


15.41 per B.H.P. 

1,200 



14.4 

4 4 

4 4 

1,200 

77 


13.2 

4 4 

E.H.P. 

2,000 


41 

40 

4 4 

B.H.P 

2,000 


50 

50 

4 4 

i 4 

2,000 


25-30 22 

4 4 

4 4 

900 20-90 16.5 

14.5 

4 4 

4 4 

900 


17.5 

15.5 

4 4 

4 4 

750 

242 

16.3 

15.3 

4 4 

K.W. 

2,400 


18 


4 4 

E.H.P. 


500 

500 


Westinghouse- 


Parsons. 600 
“ 600 


“ (1.635) 121 2,400 _ 

“ 29 180 2,400 90 


15.8 

11.5 


28 150 . 100 14.34 12.48 

28 150 . 0 15.86 13.89 


4 4 
4 4 


B-H.P, 

4 4 


Flow of Steam through Nozzles. Zeuner’s formula for the velocity 
of steam flowing through a nozzle and expanding adiabatically may be 
simplified to the following form without involving appreciable error: 

v (in ft. per sec.) = 224V / /i —/q+/s —Zi«i (1), where h and h\ are the initial 
and final heat in the water in B.T.U., l and l\ the initial and final latent 
heat in the steam in B.T.U., and s and sj are the initial and final degrees 
of saturation of the steam. 

«! = $ — (t — #i)(c — t)x- 10 -7 (2), where Sj = saturation after adiabatic 

expansion, s = initial saturation, t and t\ are temperatures (F °) before 
and after expansion. 

Values of c and x. (s is assumed or ascertained beforehand.) 

When s = 1 .95 .90 .85 .80 .75 .70 

c = 900 870 845 833 817 770 710 

16.6 15.7 14.7 13.4 12 11.5 11 


The weight of steam delivered per sq. in. of nozzle cross-section per 
minute in lbs., w = 0A17 vsu (3), where w = cu. ft. in 1 lb. of dry steam 
at the pressure corresponding to v. 

At that section of the nozzle where the pressure has dropped to 58% 
of the initial pressure the flow per sq. in. is greatest, hence this section is 
the smallest and the nozzle diverges from this point to the mouth. 

The theoretical minimum weight of steam per H.P. hour, W = 127,000,000 
- i-v 2 (at mouth) (4). 

(The foregoing matter has been derived from an article by A. M. Levin 
in Am. Mach., 6-30-04.) 

Example—Steam at 185 lbs. (absolute) containing 20% of moisture 
(s = 0.8) is required to expand adiabatically in a nozzle to 1 lb. (absolute). 

V at throat = 185X0.58 = 107.3 lbs. From formula (2) and steam-tables 
the following values are found 


V- 

Initial. . 
Throat. 
Mouth. „ 


lbs. 


l. 

8. 

u. 

h. 

185 

375 

848 

0.800 

2.45 

348 

107.3 

333 

879 

.778 

4.08 

304 

-f 

J. 

102 

1,043 

.655 

334 

70 


Substituting in (1) and (3), v at throat = 1,391 ft. per sec., v at mouth = 
3,703 ft per sec., w at throat = 182.75 lbs. per sq. in. per min., and w at 
mouth = 7.058 lbs. per sq. in. per min. 

Area of cross-section at mouth = (182.75 = 7.058 = 25.9) X section at 
throat. Min. wt. of steam per H.P. hour (from (4)) = 9.27 lbs. The 
kinetic energy of 1 lb. steam = v 2 + 2g) if v = 3,703, kinetic energy = 213,200 

ft.-lbs. , 

In designing a nozzle, calculate v at mouth from the conditions assumed — 
then a 2 (mouth) -5- 2y = kinetic energy of 1 lb. of steam in ft -lbs. Assume 
























84 


heat and the steam engine. 


this energy to develop from 0 at the inlet to its full value at the mouth 
by equal increments per increment of nozzle length, and plot euixe 
velocities corresponding thereto. Assume several pressures between 
supply and mouth and find the corresponding velocities from (1), locating 
these pressures vertically under the corresponding velocities on the curve, 
and draw a second or pressure-curve through these points Determine 
s, h, l, and u from steam-tables and formula (2) and find values of w by 


formula 1 (3) for the various pressures chosen. The reciprocals of w will 
be the sq. in. of cross-section per lb. of steam per min., which, it plotted, 
will give points in the curve of nozzle cross-section. 

(For an elaboration of this subject, consult Stodola s The bteam tur¬ 
bine,” translated by Dr. L. C. Loewenstein, D. Van Nostrand Co.) 


LOCOMOTIVES. 


Train Resistance. + 3 ^ (European practice, Fowler’s 

T 7 

Pocket Book); ^ = 3 + — (Baldwin Loco. Wks.); R x = 4 + 0.005FM- 
(0.28 + 0.03iV)-jA (Wellington); Ri = 4 + J^q (Wellington, for any load- 

ing, 5 to 35 mi. per hr. );^ = 3 + .0386 V + 1-036) YoOO (Von Bomes) - 

In these formulas R\ =resistance in lbs. per ton of 2,000 lbs. (2,240 lbs. 
for first formula), V = speed in miles per hour, N = number of cars in train, 
W = weight of train in tons of 2,000 lbs., and w = wt. of one car in tons. 

Resistance due to grade in lbs. per ton (2,000 lbs.), /£ 2 = 0.3788G ! , where 
(5 = grade in feet per mile. 

Curve resistance, in lbs. per ton, Ra = 0.5682.4 , where A = angle of curve 
in degrees. (The angle of a railwav curve is the angle at the center sub¬ 
tended bv a chord of 100 ft. The radius of a curve of A degree = 


5,729.65 ft. —A A j 

Acceleration resistance (due to change of speed), /?4 = 0.0132(T' r j 2 — / 2 ), 
where Vi is the higher speed. 

Total resistance, R = Ri~\- R? + Ra+ R*. ttt t t 

Horse-Power = ( WVR X5,280) -i- (33,000 X 60) = 0.00266617 VR 
Tractive Power cannot exceed the adhesion, which varies from 20 /o 
of the weight on the drivers when rails are wet or frosty, to 22.5% when 
drv. At starting 25% may be attained by the use of sand. 

Tractive power = d 2 p 1 s-^d 1 , where d and c?i are respectively the diams. 
of cylinder and drivers in in., p\ the mean effective pressure in lbs. per 
sq. in., and s = stroke in in. M.E.P. = boiler pressure pXc (approx.). 

Values of c: 


Cut-off = . . 
c =. 


i 

0.2 


i 

0.4 


^ -j- 1 

0.55 0.67 0.79 0.89 0.98 1 


The average m.e.p. decreases as the piston speed increases, as shown 
in the following from Bulletin No. 1, Am. Ry. Eng. & Maintenance of 
Way Assn.: 


Piston speed (ft. per min.). 250 300 400 500 600 800 1,000 1,200 
M.E.P. (%). 85 80.2 70.8 62 54 40.7 31.6 26 

For compound engines of the Vauclain 4-cyl. type, Tractive power in lbs 
= 7Js(2.66D 2 + d 2 )-^4d 1 , where p = boiler pressure, and D = diam. of high- 
pressure cyl. (For a 2-cyl. or cross-compound, omit d 2 from formula.) 

The tractive power decreases as the speed increases, as shown by the 
following table, where r = stroke-ndiam. of driver, and a speed of 10 mL 
per hr. is taken as unity. 


F =. 

10 

15 

20 

25 

30 

fr = 0.429). . 

1 

.88 

.75 

.64 

.53 

(r = 0.536). . 

1 

.83 

.67 

.54 

.45 








85 


LOCOMOTIVES. 


Weight of Train in tons, for average freight work (including engine 
f< r n . ( ‘ er ) h = tractive power h- [6 + 20 X (grade in per cent)]. The weight 
ot freight carried may be taken as (JE-wt. of 1oco.)h-2. H.P. = Tractive 
power X Eh-375. 

(.rate Area in sq. ft. = d 2 s h- C (d and s in in.). For express locomotives, 
simple, C = 197 to 288 (average practice = 240); compound, C = 118. For 
lreight locomotives, simple, C' = 250 to 290 (=500 for very heavy locos.); 
compound, C = 132 to 197 ( = 177 for good practice). (For compound 
locos. d==diam. of h. p. cyl.) 

H e atm£ Surface = Grate areaXC. For passenger locomotives, C = 
47 to 7 d (=70 for good practice). For freight locos., C = 65 to 100 (best 
practice on heavy locos., C = 78 to 90). 

Diameters of Cylinders. d = 0.542^diic-r-ps, where w = weight on 
in .l‘ :)S ' Lor the diam. of h. p. cyl. in a compound engine replace 
O.o42 in formula by 0.4 to 0.46. Diam. of 1. p. cyl. = (1.56 to 1.72) X 
diam. h. p. cyl. 

Areas of Steam-Ports. For simple locos., A =7.5% of cyl. area. 

For heavy, modern freight locos., A = 10% of area of h. p. cyl. and 4.5 
to 6.5% of 1. p. cyl. area. 

Areas of Exhaust-Ports, simple, about 2.5 Xarea of steam-port. 

Piston-Valves. . Diam. of valve = 0.4Xcyl. diam. 

Coal Consumption. From 120 to 200 lbs. per hour per sq. ft. of grate 
area. 


Under favorable conditions one I.H.P. requires the combustion of 4 
to 5 lbs. of coal per hour. 

Balancing. To avoid oscillations the forces and couples in a horizontal 
plane due to the inertia of the reciprocating parts must be eliminated 
as far as possible. 

Let IE = combined weight of crank-pin, connecting-rod, cross-head, 
piston-rod and piston + one-half the weight of one crank-arm. (In th e 

case of an inside cyl. take the weight of one web in place of ( i ran ^ c atm ^ * 

Jj 

r = radius of crank; 72 = radius of c. of g. of balance-weight; a = distance 
between centers of wheels (i.e., c. to c. of rails); 6 = distance between 
cente rs of cyls. Then, the weight of each balance-weight, Wb = 



W r ifa 2 + b 2 
aR * 2 ' 


and tan 6 


a — b 
a + b’ 


where 0 = angle between radius to c. of g. 


of balance-weight from wheel center, and the center line of the near crank 
produced. For inside cyls. both balance-weights fall within the quadrant 
bounded by the produced center lines of the cranks. For outside cyls. 
tan d is negative and the balance-weights are outside of the said quadrant. 

In the U. S. the balance-weights are equally divided between the wheels 
coupled together; in England they are concentrated on the drivers. The 
U. S. method reduces the hammer-blow on the rails, and to still furthei 
lessen this, some builders balance only 75% of the reciprocating weight. 

Another rule is as follows: On the main drivers place a weight equal 
to one-half the weight of the back end of the connecting-rod plus one- 
half the weight of the front end of connecting-rod, piston, piston-rod, 
and cross-head. On the coupled wheels place a weight equal to one-half 
the weight of the parallel-roc! plus one-half the weights of the front end 
of the main-rod, piston, piston-rod, and cross-head. Balance-weights 
to be opposite the crank-pins and their centers of gravity must be at the 
same distances from the axles as the crank-pins. 

Friction of Locomotives. An 8-wheel Schenectady passenger loco¬ 
motive tested by Prof. W. F. M. Goss gave the following results. (Cyl. 
17X24, drivers, 63 in., wt., 85,000 lbs.) 


Cut-off at i stroke, friction at 15 mi. per hr. = 12% of total power. 


4 4 4 i ^ 4 4 

4 4 

“ 55 “ 

“ “ =23% “ “ 

4 4 

“ “i “ 

4 4 

“ 15 “ 

“ “ = 7 4 % “ “ 

4 4 

“ “ ^ “ 

4 4 

“ 55 “ 

“ “ =15.7%“ “ 

4 4 



r 








Dimensions of Modern Locomotives 


86 


HEAT AND THE STEAM ENGINE. 


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* Serve tubes have internal longitudinal ribs which render cleaning difficult, but on account of increased surface they have 
n 30 to 50% greater efficiency. 

t 4-4-2 indicates wheel arrangement, thus: 4 front truck wheels,—4 drivers,—2 trailers. 





























steam-boilers. 


87 


STEAM-BOILERS. 

Horse-Power. The capacity of a boiler is fully expressed bv statinir 

gheS c“ d fio°„s W and r thVHP P Sf‘ft ° f f a'gfv™ tK 

on the economy nf chi , • ‘ ■ the steam so generated depends entirely 
on tne economy ot the engine in which it is used. There is hnwovor 

a commercial demand for rating boilers in terms of IT Pane? the ASM I’ 
committee has recommended the following: The unit of commercial H P 
developed by a boiler shall be 34.5 lbs. of water evaporated per hour from 

?„ ! ?V er ' tempera Ure of 212 ° F - into dr y steam of the same tempe?^ 

ture, hich is equivalent to 33,317 B.T.U. per hour and also DraS fv 

?? l 7 n^K nt t0 aU evaporation of 30 lbs - of water from 100° F. into steam 
at 70 lbs. gauge pressure. 8ieam 

Heating Surface is all that surface which is surrounded on one 

Ilelthi surf e a r ce°in b ?q he H t6< 1 ° u 0t h ° n by flam ? or heated ^ases. 

xieaimg sunace in sq. it., A-cQ-t-H, where Q = quantitv of water evan 

prated per hour, H = total heat of the steam at boiler pressure and c for 

locomotive boilers -90, for Scotch marine boilers = 180, for Cornish = 220 

f T?oi ai £ c y^‘i lder - 28 0» for return-tubular and water-tube boilers = 400 

Relative Values of Heating Surfaces per sq. ft. compared with flit 

plates Mat plate above fire, 1; cylindrical surface above and concave 

to file, 0-95; same, but convex, 0.9; flat surface at right angles to the 

current of hot gases, 0.8; water-tube surface, same as last 0 7- slonintr 

?,f ffr^ e fiV 1 ? 6 of a i nd in K Cli T ed the fire ’ 0.65; verLcal surface at sidf 
^ r ®*i 0.5, loconmtiye boiler tubes,—not more than 3 ft. from fire-box 
tube plate, 0.3. Horizontal surfaces underneath the fire and the lower 

h Rat n in f 7u L- hea 6 c f i lbes fre not considered as effective. 

Ratio of Heating Surface to Grate Surface. Plain cylinder 10 
to 15 Scotch marine and Cornish, 25 to 40; Lancashire, 26 to 33- hori 
to 9^0 return 'f u bular, 30 to 50; water-tube, 35 to 65; locomotive, 60 

Aieas of Tubes and Gas Passages. Area near bridge wall = l grate 
nu’ tn T nn y ea / tota1 ^ 0, l to O.llXgrate surface for anthracite and 
combustion (BaSs e ). area b,tUm,nous e0 “ b both moderate rates of 

only - 5 ' 000 to 6 - 000 lbs - ; 

Boiler Efficiencies. For the purpose of comparison it is customary 
to express the evaporation m lbs. of dry steam per lb. of pure combustible 
and m order to eliminate the effects of variation in the temperature of 
the feed-water, the results are reduced to what is termed “the equivalent 
evaporation from and at 212° F. (See page 59.) The complete combuS 

of 1 lb. of pure carbon will evaporate ^|y = 15.3 lbs. of water from 

a?d in oi 2 ,d 192 American boiler tests summarized by H. H. Suplee 
give 10.86 lbs. per lb. of fuel, which may be considered as good practice 
ordinary averages being from 6 to 8 lbs. per lb. of fuel. 12.5 lbs. evaporation 
is generally the best obtainable from high-grade fuels like Pocahontas 
and Cumberland coals One-test, however, is recorded showing an evapora¬ 
tion of 13.23 lbs. per lb. of Cumberland coal. 

Performance of Boilers (D. K. Clark). w = Ar* + Bc, where w = lbs 
water evaporated from and at 212° F per sq. ft. of grate per hour, r = ratio 
of heating to grate surface, and c = lbs. fuel per sq. ft. of grate per hour 
A and B are respectively as follows: Stationary boilers, 0.0222 and 9 56- 
marine, 0.0-6 and 10.25; portable, 0.008 and 8.6; locomotive, 0.009 and' 

Materials and Tests. (From Am. Boiler Mfrs. Assn. Uniform Speci¬ 
fications.) ^ 

Cast Iron. Should be soft, gray, and highly ductile; used only for 
hand-hole plates, man-heads, and yokes. 

Steel. Homogeneous open-hearth or crucible. 

? K 0t eXpOS ? d to , dire ?* heat. Tensile Strength (T.S.) 
am“suiph 7 u 0 r'“7<0.0 r 35% q ' m - : e, ° n *» U °" > 2i% in 8 *“• Phosphorus <P> 

l ° 65 - 000 lbs - 



83 


HEAT AND THE STEAM ENGINE. 


Fire-Box Plates (exposed to direct heat). T.S. — 55,000 to 62,000 lbs., 
elongation>30% in 8 in., P<0.03% and S< 0.025%. . . . , 

Test Pieces to be 8 in. long with a cross-section >0.5 sq. in.; widtn — 
or> tnickness, edges machined. Up to 0.5 in. thickness, plate must 
stand bending double and being hammered down flat upon itself. Above 
0.5 in. it must stand bending 180° around a mandrel of diam. — 1.5/. trend¬ 
ing-test pieces must not be less than 16t in length, edges must be machined 
and pieces must be cut both lengthwise and crosswise from plate. 

Rivets must be of good charcoal iron or of soit mild steel having same 
properties as fire-box plates. They must be tested hot and cold by driving 
down on an anvil with the head in a die, by nicking and bending and by 
bending back on themselves cold, all without developing cracks or Haws. 

Tubes to be of charcoal iron or mild steel made for this purpose, lap- 
welded or drawn. Tubes must be round, straight, free from blisters, 
scales, and other defects and tested under an internal hydrostatic pressure 
of 500 lbs. per sq. in. Standard thicknesses (B.W.Gj:—No. 13 for 1 to 
If in. tubes, No. 12 for 2 to 2* in., No. 11 for 2| to 3£ in., No., 10 for 3£ 
and 4 in.. No. 9 for 44 and 5 in. , , , , . , 

Tube Tests. A section cut from one tube selected at random rom a 
lot of 150 or less must stand hammering down vertically when cold with¬ 
out cracking or splitting. Tubes must also stand expanding flange over 
on tube plate. 

For tubes.1 to If 2 to 2* 2£ to 3* 3* to 4 4* to 5 in. in diam. 

Length of test piece = £ 1 1£ U . If in. 

Stay Bolts of iron or mild steel must show on an 8 in. test piece as 
follows- Iron, T.S. >46,000 lbs., elastic limit >26,000 lbs., elongation>22% 
for sections under 1 sq. in. and >20% for larger sections 

For steel these values are respectively >55,000 lbs., >33,000 lbs., >25%, 


Tests. A bar taken at random from a lot of 1,000 lbs. or less and threaded 
with a sharp die to a V thread with rounded edges must bend cold 180° 
around a bar of same diam. without developing cracks or flaws. Another 
bar, screwed into a well-fitting nut of the material to be stayed and riveted 
over, must be pulled in a testing machine. If it fails by pulling apart 
its strength is measured by the T.S. If failure is due to shearing, the 
measure of strength is the shear stress per sq. in. of mean section in shear. 

(Mean section = * ° f ^ la — Xcircumf. at half height of thread.) 

Braces and Stays to be of same material as stay bolts. T.S. to be 
determined from a 10 in. bar from each lot of 1,000 lbs. or less. 

All bending and hammering tests indicated above must develop no flaws, 
cracks, splitting, opening of welds, or any other form of distress. 

Workmanship and Dimensions. Flanging, bending, and forming 
should be done at suitable heats, no bending or hammering, however, 
being allowed on any plate which is not red by daylight at the point worked 
upon and at least 4 in. beyond it. Rolling to be by gradual increments 
from the flat plate to a true cylindrical surface, including the lap. The 
thickness of bumped or spherically dished heads should equal that of a 
cylindrical shell of solid plate whose diam. is equal to the radius of curva¬ 
ture of the dished head, an increase of t being taken to allow for rivet 
holes, manholes, etc. , . . , , . . . 

Rivet holes should be perfectly true and fair, either drilled or cleanly 
punched, burrs and sharp edges to be removed by slight countersinking 
and burr-reaming both before and after sheets are joined. Under sides 
of original rivet heads to be flat, square, and smooth. Allow length of 
14 diam. for stock for heads, for £ to H in. rivets, and less for larger.sizes. 
Allow 5% more stock for driven head for button-set or snap rivets. For 
machine-riveting, total pressure on die = 35 tons for £ in. rivets, 57 tons 
for is in. rivets, 65 tons for 1 in., and 80 tons for 1£ and 1£ in. rivets. Ap¬ 
proximately, make d of rivet hole = 2< (of thinnest plate), p" = 3d, distance 
between pitch lines of staggered rows = 0.5p", lap for single-riveting = p", 
lap for double-riveting = 1.333p" (add 0.5p" for each additional row of 
rivets). For exact dimensions make resistance to shear of aggregate rivet 
section = >1.1 XT.S. of net metal. Holes <£ in. in steel may be punched, 
above £, punch and ream, or drill. Drift-pins to be used only to pull 
plates into position,—never to enlarge holes. Calking to be done only 




STEAM-BOILERS. 


89 


with found-nose tools, calking edges to be planed, sheared, or chipped 
to a bevel. Finishing may be done with a square-nose tool if care is taken 
to avoid nicking the lower plate. Safe working pressure per sq. in. on 
flat surfaces p = Ct 2 -i-(p") 2 , where £ = thickness of plate in ltiths of an 
inch, 7?" = pitch of stays in in., and C = 112 for plates fa in. anil less, with 
riveted screw stays, 120 for platesin. with riveted screw stays, and 
140 for all plates where the screw stays have in addition a nut inside and 
outside the plate. This latter is imperative when the feed-water contains 
salt, acids, or alkali. 

Tube holes should be punched i in. less than tube diam. and reamed 
or drilled, holes being slightly countersunk on both sides. Finished holes 
to be from to rg in. larger than tube, according to size. If copper ferules 
are used, the ferules should be a neat fit in the holes. The tube sheet 
should be annealed after punching and before drilling, and the tube ends 
before setting. Tubes to project re in. beyond sheet for each inch ef 
diam. Tubes to be expanded only until tight. Ends which are exposed 
to direct flame must be flanged, beaded over and slightly re-expanded 
Copper ferules (No. 18 to No. 14 wire gauge) to be used in fire-tube boilers 
on ends exposed to direct heat. Stay bolts to be carefully threaded and 
holes tapped with a tap extending through both plates. Bolts to project 
k diam. for riveting over. Tnickness of nuts for screw stays >0.5 diam. 
of stay. Pitch of stays <10 in. If welding is necessary in braces and 
stays take strength of welded bar = 0.8 X strength of solid bar. Brace 
rivets subject to oblique pull are allowed to bear only one-half the stress 
of seam rivets. Manholes to be flanged inwards on a radius >3< and 
are to be reinforced by W.I. or steel rings, which are shrunk on. Domes 
when unavoidable to be flanged down to shell, and the shell to be flanged 
up inside the dome or else reinforced by a collar flanged at the joint, flanges 
being double-riveted. Drums to be put on with steel collar flanges >1 in. 
thick, double-riveted to shell and drum and single-riveted to neck or leg, 
or, the flanges may be formed on the legs. 

Safety factors rivet seams, 4.5; flat surfaces, bumped heads, stay- 
bolts, braces and stays, 5. Hydrostatic test pressure should not exceed 
the working steam pressure by more than £ of itself, and this excess should 
not be greater than 100 lbs. per sq. in. The temperature of testing water 
should not be less than 125° F. 

Board of Trade (B. T.) and U. S. Statute Proportions and Rules. 

3Iaterials. Shells; (B.T.) T.S. from 27 to 32 tons, elongation in 10 in. > 18% 
(if annealed, >20%); 2 in. strips to stand bending until sides are parallel 
and not >3* apart. (U.S.) When * = or<0.5 in., contraction must be = 
or>50%, from 0.5 to 0.75 in.,>45% and above 0.75 in.,>40%. 

Stays (B.T.). Same T.S. as shells, elongation in 10 in.>20%. Steel 
stays welded or worked in fire not to be used. Allowable load = 9,000 lbs. 
per sq. in. on net section. (U.S.) Reduction of area must be >40% if 
test bar is >0.75 in. in diam. Allowable load = 6,000 lbs. per sq. in. 

Notation for the following Boiler Proportions D = boiler diam., t = 
thickness, ^thickness in lGths, p = greatest pitch between stays, L = 
pitch of flanges, d = outside diam. of tubes, W = width of flame box, = 
length of girders, p! = pitch of bolts, D 2 = distance between centers of 
girders, d x = depth of girders, / 2 = sum of girder thicknesses, D 3 = least 
horizontal distance between centers of tubes, d 2 = inside tube diam , If ,— 
width of combustion box from tube-plate to back of fire-box; all in 
inches. P and T are working pressure and tensile strength in lbs. per 
sq in <S = surface supported in sq. in., Z>i = outside flue diam. in ft., 1 = 
length' of furnace (up to 10 ft.) in feet, E = safety factor, = 4.5, ^per¬ 
centage of strength of joint compared to solid plate. 

Buffer Shells (B.T.). P = 2BTt + DF. (U.S.) P = Tt + 3D for single¬ 
riveting. Add 20% for double-riveting. 

Flat Plates (B.T.). P = C(ft + l)* + (S-6). + + 

C = 125 for plates not exposed to heat or flame, stays fitted with nuts 
and washers, the latter at least 3 Xdiam. of stay and having a thick¬ 
ness = it of plate. , , 

= 187.5, same, but with diam. of washers = f pitch of stays, and ot 
thickness not less than that of the plate. 

= 200 same, but with doubling plates in place of washers, whose 
width = 4 X pitch of stays, and thickness = that of plate. 

= 112.5, same, but stays fitted with nuts only. 


90 


HEAT AND THE STEAM ENGINE. 


C = 75 for plates exposed to heat or flame, steam being in contact with 
the plates, stays fitted as where C = 125, above. 

= 67.5, same condition, but stays fitted with nuts only. 

= 100 for plates exposed to heat, or flame, water being in contact with 
the plates, stays screwed into plates and fitted with nuts. 

= 66, same condition, but stays with riveted heads. , 

(Above values for steel plates; for iron plates take 80% of same.) 

C=G12 for plates in. and under, with screw stay bolts and nuts, 
with plain bolt fitted with single nut and socket, or with riveted 

head and socket. ... f , 

= 120 for plates thicker than * in. for same fastenings. 

= 140 for flat surfaces, stays fitted with inside and outside nuts 
= 200 same as for C = 140, but with the addition of washer riveted 
to plate, whose thickness is at East 0.5Z of plate and whose diam. 

= 0.4 X pitch of stays. . , . , , , , , -,r, 

NB Plates fitted with double angle-irons and riveted to plate with 
leaf at least it of plate and depth at least iX pitch are to be allowed the 
same pressure as that determined for plate with washer riveted on. 

No brace or stay bolt in a marine boiler to have a pitch greater than 
10.5 in. on fire-boxes and back connections. 

Plates for Flanging (B.T.). p = ^_00* (5 _ __12). This formula is 

■ 12 , 


d V 60* 

for the strength of furnaces stiffened with flanged seams where L< 120<- 
the flanges being properly designed and formed at one heat 

Furnace Flues. Fong furnaces (B.T.). P = Ct~ — (Z-hl)^!, where 
ZX115* —1). C = 88,000 for single-strap butt-joints single-riveted, 
= 99 030 for welded joints or butts with single straps double-riveted, 

and also for double-strap butt joints single-riveted. , , ._ 

p from above formula should not exceed the value given by the following 
formula for short and patent furnaces. » _ , 

Short Furnaces, Plain and Patent (B.T.). P — ct '■ D,, where c 
8 800 for plain furnaces; =14,000 for Fox (max. and mm. * = f and ts m. 
and plain part<6 in. long); =13,500 for Monson, same conditions as 
p ox . =14,000 for Purves-Brown (max. and mm. Z = £ and ye m., plain 

Long Furnaces (U.S.). P = 89,600* 2 = /Di (Z not to exceed 8 It.). 
Short Furnaces (U.S.). P = ct + D u where c= 14 000 for Fox CD,- 
mean diam.); =14,000 for Purves-Brown (D, = flue diam.); =5.6, 7 for 
niain flues >16 in. diam. and <40 in. diam. when not over 3-foot lengths. 

Stay Girders (B.T.j. P = Ce? 1 2 / 2 -r-(TF —pi)_D 2 Z,, where C — 6,600 for 
1 bolt =9 900 for 2 or 3 bolts and =11,220 for 4 bolts^ 

Tube Plates (B.T.). P = 20,000Z(D 3 -d 2 )-*- WyD z . Crushing stress on 
tube plates caused by pressure on top of flame-box to be <10,000 lbs. 

' Air'passages through grate bars should be from 30 to 50% of grate 
a"ea the larger the better, in order to avoid stoppage of air supply by 
clinker, but with clinkerless coal much smaller areas may be used. 

COMBUSTION. 

Combustion or burning is rapid chemical combination accompanied 
bv heat and sometimes light, during which heat is evolved equal to that 
required to separate the elements. 

In the burning of a simple hydrocarbon (e.g., marsh gas), the combus¬ 
tion being complete, ., . _. r , v 

Marsh Gas + Oxygen = Carbon Dioxide 4- W ater (Steam); 

CH 4 + 20 2 = CO a + 2H 2 0 

or taking the atomic weights of C, H, and O as 12, 1, and 16, respectively, 
(12 + 4)+ 2( 16X2) = [12 + (16 X 2)] + 2(2 + 16), 

i.e., 161b. + 64 1b. = 44 1b. + 36 lb 

or 1 lb. + 4 lb. yields 2.75 lb. + 2.25 lb. 

Also 1 lb. C burnt to C0 2 yields 14,600 B.T.U. and 1 lb. H burnt to H z O 
yields 62,000 B.T.U., and, as 1 lb. CH 4 = f lb. C + i lb. H, then 
y 0.751b. C + O yields 14,600X0.75 = 10,950 B.T.U. 

0.25“ H + O “ 62,000X0.25 = 15,500 “ 


Total=20,450 





COMBUSTION. 


V 1 


91 


■ j, 


Experimentally, about 2,800 B.T.U. less are obtained, the loss being 
required to effect the work of decomposing the C and H. K 

oo bituminous coal contains on the average, by weight Carbon 

elemen; s “;t r 75%: 4 ' <i%; ° Xree ”' 315 %’ Nitroge^a'n/sufpC (LZt°ve 

■ 10 e° ^ bs ' fuel tlle 315 lb. O is already united to (&X3+5) 0 4 lb II 

i&sn Mr* ■" 

wBhli li'o^rsft^orf^b 0 ‘toSSl, 12 ’ 66 * “ d 2 ">• H Unite 

83.5 lb. C require 83.5X2.66 = 222 lb O 
4.2 “ H “ 4.2X8 = 33.6 “ 


Or, for 100 lb. coal, total = 255.6 “ “ 

Air = 23% 0 + 77% N; therefore 23 100::255.6-h 100 111 or 11 1 lb 
of air are theoretically needed for the combustion of 1 lb. of the coal' (In 
practice the theoretical amount must be multiplied by 1.5 for gas furnaces 
by 1.5 to 2 for good grates, and by 3 or more for defective furnaces ) Also' 
0.835 lb. 0X14,600=12,191 B.T.U. 

0.042 “ HX 62,000= 2,604 


Total B.T.U. per 1 lb. coal = 14,795 

The Calorific Value of a Given Fuel may be expressed by the follow¬ 
ing modification of Dulong’s formula: 

B.T.U. per lb. = 14,600 0 +62,000 (h-^)+ 4,000 S, where the pro¬ 
portions of C, H, O, and S are determined by analysis. 

Where a complete analysis of the coal is not obtainable the following 
formula of Otto Gmelin may be used B.T.U. per lb. = 144[100 — (?c + a)]— 
10.8 wc, where w and a are the percentages of water and ash, and c is a 
constant varying with the amount of water. When w<3%, c = 4- when 
w is between 3 and 4.5%, c = 6; w bet. 4.5 and 8.5%, c=12; w bet, 8 5 
and 12%, c=10; w bet. 12 and 20%, c = 8; w bet. 20 and 28%, c = 6- 
re>28%, c = 4. Also, when C and C x are the percentages of fixed and 
volatile carbon, respectively, and H the percentage of hydrogen, BTU 
per lb. = (14,600 C + 20,390 Cj + 62,000 H) = 100. . 


American Coals. Approximate Analyses and Calorific Values. 



Mois¬ 

ture. 

Volatile 

Matter. 

Fixed 
Carbon. 

Ash. 

Sul¬ 

phur. 

B.T.U. 
per Lb. 
Coal. 

Anthracites: 







* E. middle field, Pa. . 

4.12 

3.08 

86.38 

5.92 

0.49 

13,578 

* N “ “ “ . . 

3.42 

4.38 

83.27 

8.20 

.73 

13+34 

W. “ “ “ . . 

3.16 

3.72 

81.14 

11.08 

.90 

12,958 

Semi-anthracite: 






Loyalsock, Pa. 

1.3 

8.10 

83.34 

6.23 

1.03 

14,247 

Semi-bituminous. 






* Clearfield, Pa. 

.81 

21.10 

74.08 

3.36 

.42 

14,985 

* Cumberland, Md. . . 

.95 

19.13 

72.70 

6.40 

.78 

14,461 

* Pocahontas, Va. . . . 

.85 

18.60 

75.75 

4.80 

.62 

14,854 

* New River, W. Va. . 

.76 

18.65 

79.26 

1.11 

.23 

15,429 

Bituminous: 






* Youghiogheny, Pa.. 

1.03 

36.49 

59.05 

2.61 

1.81 

14,262 

Connellsville, Pa. 

1.26 

30.10 

59.61 

8.23 

.78 

13,946 

Brazil, Ind. 

8.98 

34.49 

50.30 

6.28 

1.39 

12,356 

* Big Muddy, Ill. 

7.7 

31.9 

53 

7.4 

. . 

12,895 

Streator, 111. 

8.3 

37.63 

45.93 

8. 14 


12,047 

Rosyln, Wash. 

6.34 

37.86 

48.30 

7.59 

.49 

12,429 

(Cle-Elum.) 

Cokes: 





Connellsville, Pa. 

(B.T.U. 

pr. lb. = 

88.96 

9.74 

.81 

12,988 

Chattanooga, Tenn... 

%cx 

14,600) 

80.51 

16.34 

1.595 

11,754 

Birmingham, Ala. . . . 



87.29 

10.54 

1.195 

12,744 

Pocahontas, Va. 

.... 


92.53 

5.74 

.597 

13,509 

































02 


HEAT AND THE STEAM ENGINE. 


the amount of combustible in the coal. 

V alues of a 

1'7.™™- 26|» 2§0 £§0 l||o 1 SM 0 

<1'"-^So 16920 “mso 15,000 14,400 

mv,; a formula is fairlv accurate where the percentage of fixed carbon 
is Ibive 60? whenever exact results are required a ca onmetoc determina- 
tion of the heating value of the particular fuel should be made. 

Wood 1 cord = 128 cu. ft., about 75 ft. of which are solid wood. 2.25 
lb' of d^y wS5 are about equal to 1 lb of soft coal m heating effect. 
Average wood (perfectly dry) has a calorific value of about 8 200 B^l.u. 
per lb g f « ordinary, air-dried (25% moisture) about 5 800 B f U. per ft 

ft C 520 P JlsTB;a O S, + ?ex 3 .: ?™d°e°oil, 1»6 

B »£tiilates from Petroleum (CioH,, to from 71.42^(0 

7 77% C and from 28.58 to zo.^o /o xi. op. u non +r> 

BoUing-point varies from 86° to 495° F. B.T.U. per lb., from 2/ ,000 to 

28 ras‘Fuels (B T.U. per 1,000 cu. ft.): Natural gas, 1,100,000; c _°al-gas, 
640 000 to 675,000; water-gas, 290,000 to 327,000 ,gasoline-gas, 517,000, 

Pr0 ^scXn^us th F r uels e ’ ^K^Seif 'Shark, 4,280 (30% 

water) to 6 100 (dry); straw, 5,400 to 6,500; bagasse (sugar-cane refuse), 
3,750, when fibre = 45%; corn, 7,800 (ordinary condition) to 8,500 (dry). 

Draft. Chimneys. T m u u v.. 

Kent. Gale-Meier. Ing. Taschenbuch 

0.06F 0 07Diam., d = 0.242F 

Area, A.- 

/o.oefy 120 (Fy 0 .2i6(£-) 2 +w. 

Height, h .■=■ V, ^ / t 'G' _ '(? 

Where F = total coal burnt per hour in lbs < = temp of discharge gases 
in F ° Cr = sq. ft. of grate area, d = internal diam. in feet (A in . q. ., 
in ft’)’ The larger results obtained from the Taschenbuch formulas are 
probably due to the inferior evaporative power of German coals 

Intensity of Draft </). / in inches of water = — jr), where 

T and T< are respectively the absolute temperatures of the external air 
and ?he chimney gases. / at the base of ordinary chimneys ranges from 
0 5 to 0 75 in. In locomotives the vacuum induced by the steam-blast 
varies from 3 to 8 inches of water in the smoke-box and is about i as-much 
in the fire-box The best value of Ti = 2T 2 . or about 58o F. 

Temperature of Chimney Gases. To determine same approximately, 
suspend strips of the following metals in the chimney and note those which 

me ^‘ Metal • • Sn Bi Pb Zn Sb 

Melting-point, F.°. . 456 518 630 793 810 

Velocity of Chimney Gases. 

8^h (chimney temp.—air temp.) 
v in ft. per sec. — 3.3 Xchimney temp! 

<T f>?aft Pressures required for Combustion of Fuels (in inches 
of water). Wood, 0.2 to 0.25; sawdust, 0.35 to 0.5; do., with small coal, 














boiler accessory apparatus. 


93 


Ilok?Ti fi .* o.S- 7 t ^ : I sl 2 ^ ; k - = x d a S - t ^ e U 5 

b 'l&haKTI&tac th f ‘“V evaporative^ower A'fZl ^ 

into a hopper and pushfd forward 6 from^the^botu^ k° al is fed 

actuated plunger into thp rp*nr+ riI . f; . t ^ bottom thereof by a steam - 

duced at the fopofretortAst hf f^fh* f T beneath ,’ ™.being intro- 
beneath its gases are liberated bv thp C °^ a PP r °aches the fire lrom 

fire and areconsumed—aidinJ in pan upwards through the 

reaches the fire practically crfked th prodl Jction of heat,—and the coal 

avoided The manufacturers (Underfeed° sToke? Co^LM b 7 
claim that its use will effect a saving of from 18 to 25% of Q t0) 

pared with hand-firing. s m to 30/ 0 ot the fuel as com- 

BOILER ACCESSORY APPARATUS 

^ Saviiig m per cent by heating feed-water with exhaust steam = 
H-hi where H== total heat of 1 lb. steam at boiler pressure, h t = total 

heater!^ 1 lb ‘ Water bef ° re entering heater - and ^2 = same after leaving 

or average conditions there is an approximate savincr r»f i o/ frw « u 
merest 11" in the temp, of feed-wa^, 0 which Wgh 

Creen’s Economizer is a feed-water heater composed of tubes so 
f in f f^ dues between boiler and chimney as to intercept some of 

900 iK at ° f the waste gases - As the temperature of steam from 100 to 

fh?we b thL r fl SUre rangeS from 338 °, to 388 ° F - a " heat in chimney gases 
abj\e these temperatures is wasted unless a portion of it can be absorbed 

in To° me s V* c h manner. Average chimney temps, reach 600° F. 

i.P n i!. n9zers efteet a gain in evaporative power of from 6 to 30% fair 
to S 250° p Ging SGt at 10 t0 12 %’ witb a cool mg of flue gases of from’l50° 

r, Q S 9 o I ? denSerS * • lT i condensil ?g the exhaust steam from an engine a 
partial vacuum is formed and the gain in power may be based on the 
increase of the mean effective pressure by about 12 lbs. per sq in 

?eTp“ y f 30XWt - °' S,eam be 

Surface Condensers should have vertical brass tubes for maximum 
efficiency and the water should flow downwards through them. Tubes 
should be as long as practicable and of small diam. (0.5 to 1 in.). Cooling 
surface of tubes — 1 to 3 sq. ft. per I.H.P., according to climate. 12 5 lbs 
condensed per sq. ft. per hour is good practice. Q of circulating 
water —30 Xwt. of steam condensed. s 

Q for jet condenser in lbs. = ^-V Q for surface condenser = —~ l , where 

l f rVl 4 ° F - = total heat of 1 lb.Exhaust steam, t = temp. of 2 hot-well in 
1 -.^-entering temp, of cooling water, and t 2 = temp. of water when 
i ea Xy^ g the concIens e. r - Area of injection orifice =lbs. water per min.-r-650 
to 750, or, =area of piston -h 250. 

Evaporative Condensers. In these the exhaust is led through a 
large number of pipes cooled externally by trickling streams of water 
Ihis water evaporates, thus condensing the exhaust steam in the pipes' 
which is then pumped back into the boiler. Used where economy in’ 
water consumption is imperative. In well-designed condensers of this 




94 


HEAT AND THE STEAM ENGINE. 


class 1 lb. of water will condense 1 lb. of steam, as against the 20 to 30 lbs. 
of water required in jet and surface col J d f£ t of condensation and 
th^S^Sm^l/contairSdwLn entering the b «|J e ^ n / e “ t je J f C ®“ r den The 
sii^ofan ak-punq/'is^cllcSlated^fr^thlse conditions, allow amgs^b emg 
made for efficiency. Volume of Air-Pump in cu. ft- = — (5+ Q) “r.p.m. Xci ’ 

pei^min ==cu e ^t° f .of S cooling r< water e per'min ?, c = 2 for singfe^-^Grlg^ncl 

HSSSSSfiir l'*uniDs! m CapaX g -l3Vr‘ l Mam. of cylinder in inches - 

Fffii If V: per 

Safety-Valves, Are ^JJLjoaded valves; i sq. in. per sq. ft. of grate 
sq. ft. Sp^ng-toaded valves for water-tube, coil, and sectional boilers 
area. ?. 175 ik s pressure must have an area>£ sq. in. per sq. ft. 

carrying overl 7 5 pre 5 ° to axis> Spring-loaded valves to be 

fippUed with^ liver which shall raise valve from seat to a height equal 

U at least | diam. of opening^ 5xgrate area in sq . ft.)-(gauge pres- 

suif+ 15 ). Philadelphia Rule: Area in sq. in. - (22.5 Xgrate area in 


re + 15)> rnuaaeipiiid /y t 

sq ft.) - (gauge pressure + 8.62). Ingenieurs Taschenbuch a = 0.0644 V - 

Where a-area of valve in sq. ta^per^ f‘; V ~™1 

Sector, (Live-Steam).' Water injected in gala, per hour-1.280D VP, 
wheri B-diam! of throat in ins., and P-steam pressure .n lbs per sq. m 
wliere . cu.ft. of feed-water per hour(gross) . 

Area of narrowest part of nozzle in sq.in. sqON'P ressure in atmospheres 

One lb. steam will tajertjtogt l^lb-water. 

WlU l fe a e r t v fivesteam jet can be attached to feed against 110 lbs. pressure, 
aU P hv compounding another live-steam injector with it, a boiler may 
bl'fed up tn about 200 lbs. pressure, the feed reaching boiler in this case 

at about 250° F, „„ TTin Ravine of fuel over amount required when a 

.fer ° ut — boil " ™ tin ‘ 


Injector feeding aOSOJ, J« a ^ e r a ^ m 15f) o to 200°) 
Direct-acting pump through heater (from 60 to |00 q ). 
Geared v 


saving, 


1.5% 

6 . 2 % 

12 . 1 % 

13.2% 


Steam-Pipes (B.T.). d = inside diam., *=thickness, both in inches; 

p = pressure in lb. per sq. in. ^ ^ ^ ^_ ^ 


+ in.; solid-drawn, t ■ 


6,000 


4- iu. 


Copper Pipes, brazed, t q qqq 

Lap-welded Iron Pipes, t = ^- Q \ Cast-iron Pipes, < = g; 50 o + i m - 

„ • cPmild be made for expansion in long lines, which amounts 

Provision shou 1 oe f tcmneratures usually employed. 











INCRUSTATION AND CORROSION. 


95 


INCRUSTATION AND CORROSION. 

some scale, and waters containing over 5 narts in nmlJ* trouble- 
or muriatic acids are liable to calse iri^s corros“n °° ““ nC ’ “ ,phunc - 

Prevention and Cure of Boiler Troubles due to Water, 
trouble. Troublesome Substance. Remedy or Palliative 

Incrustation. . Sediment, mud. clav. etn Filtration? blowing -off 

Blowing-off. 

Heating feed and precipitat¬ 
ing by addition of caustic 
soda, lime, magnesia, etc. 
Addition of carbonate of soda 
or barium chloride. 
Addition of barium chloride. 

Precipitate with alum or 
ferric chloride and then 
filter. 

Ditto. 

Add alkali. 

Heating feed, addition of 
caustic soda, slacked lime, 
etc. 

Slacked lime and filtering. 
Carb. of soda. (Substitute 
mineral oils.) 


Troublesome Substance. 
Sediment, mud, clay, etc. 
Readily soluble salts. 

Bicarbonates of magnesia, 
lime, and iron. 

Sulphate of lime. 

Priming.Carb. of soda in large 

amounts. 

Organic matter (sewage). 

Corrosion.Organic matter. 

Acid in mine waters. 

Dissolved carbonic acid and 
oxygen. 

Grease. 


Many scale-making minerals may be removed by using a feed-water 
heater and employing temperatures at which the minerals are insoluble 
and consequently precipitate, when they may be blown off before passing 
to boiJer. Phosphate of lime, oxide of iron and silica are insoluble at 212° 
carbonate of lime, at 302°, and sulphate of lime at 392° F 

Kerosene has been successfully used in softening and preventing scale 
and should be introduced into the feed-water in quantities not exceeding 
0.01 qt. per H.P. per day of 10 hours. 

Tannate of Soda Compound.— Dissolve 50 lb. sal soda and 35 lb 
japonica in 50 gal. water, boil and allow to settle. Use & qt. per H P per 
10 hours, introducing same gradually with the feed-water. 

Grooving is the cracking of plate surface due to abrupt bending under 
alternate heating and cooling. It is generally found near rigid stays 
and its ill effects are augmented by corrosion. It may be avoided by 
providing for sufficient elasticity along with strength and by rounding 
the stay edges at the plate 


INTERNAL-COMBUSTION ENGINES. 

Internal-combustion engines are divided into two classes. In the first 
an explosive charge of gas and air (or a vapor of alcohol, gasoline, or kerosene 
mixed with air) is drawn into the cylinder, compressed, ignited, expanded! 
and then exhausted. The ignition produces a practically instantaneous 
explosion. 

In the second class (e.g., Diesel motors) a charge of air is drawn in and 
is raised by compression to a temperature high enough to ignite the oil 
gasoline or other fuel which is sprayed into the cylinder during a certain 
portion of the po’wer stroke. The combustion in this case is gradual and 
extends over the period of the stroke during which the fuel is injected 

In simple engines there are four strokes in the cycle of operation 
1 st stroke, drawing in of explosive charge; 2 d (return) stroke, compres¬ 
sion of the charge; 3d stroke, ignition and expansion (power stroke)- 
4th (return) stroke, exhaust of the burnt gases. The 1st, 2 d, and 4th 
strokes consume from 5 to 10% of the power developed on the 3d stroke. 
(For indicator card, see Fig. 12 , T .) 




96 


HEAT AND THE STEAM ENGINE. 


1: 6 to 1: 7 

1,000 to 1,100° F. abs. 
55 " t u 
70 “ 85 

210 “ 285 


In two-cycle engines the charge ^ Outward 6 of engine 

ignition and expansion taking pi ^e , beine one impulse for each 

revolution”) alTfon^ructe'd 80 . to g ive 

an impuise on ea^h stroke^ internal-combustion engine is 

i,S by T 1 if ig “refo n? tife «* «£**■£ that 

at the end of the compression must n a^ roatAi near to tnat b.T.U. 

The temperature of ignition ^ eS ffa 1 ^ s er t S £ ef a C) S re ^ 1 7 hol Sd not be highly 
contained in the charge, and ric 1 g- ^ Q f compression may 

compressed save in well diluted charge . - 0 n as in the Banki 

be extended by cooling the gases ^ergom^heat given 

motor, where water is sprayed into% C t y i n fel°i engine where the air 
out durine compression, and also as in the JJiesei engine, vvuc ^ 

is compressed to its final pressure-before the fud w imje t l k 
Rich Gases (containing over 350 B.l.U. per eu. eucu, 

and natural gases. Rich Mixture. Lean Mixture. 

Ratio of gas to air. . .. 

Temperature of ignition. . . . 

Compression, lbs. per sq. in.. 

M.E.P. “ “ “ . 

Explosion pressure per sq. m. 

Lean Gases (containing less than 350 B.T.U. per cu. ft.), 
producer, and blast-furnace gases. 

Ratio of gas to air. . .. * *? ] : Lo F abe! 

Temperature of ignition.1,300 <( L 47 f fe F -^ in . 

Compression. .. 70 .« • « .« 

Mean effective pressure. „ .. «< «« 

Explosion pressure. J 00 > 

The gas and air should be thoroughly mixed before ignition which, 
for rich mixtures, is either by a hot tube, a valve-governed flame, or by 
an electric spark. For lean mixtures the electric spark is used. 

Liquid Fuels. 

Gasoline, 

Benzine. 

Ignition temperature, 0 F. abs. 930 to 1,020 

Compression, lbs. per sq. in.. 4n “ 

Explosion pressure, lbs. per sq. in. . . . 170 ‘ -80 

M.E.P., lbs. per sq. in. 

Liauid fuels are vaporized before mixing. Light oils (gasoline, etc.) 


1:10 to 1:15 
1,200 to 1,380° F. abs. 
75 “ 115 
65 “ 78 

285 “ 355 

Dowson, 


Kerosene, Naphtha, 
Alcohol. 

985 to 1,075 


(Diesel) 


5o 

450 

140 

50 


115 

500 

285 

70 


mav be atomized. Heavier oils require neaimg m „'i C iu 

Gasoline -gas is usually ignited by an electric spark,— heavier oils by the 

Average Values for Compression (Lucke). Kerosene and city gas, 
80 lbs lasoline, 85 lbs.; natural gas, 115 lbs.; producer gas, 135 lbs., 
Ui„„ t furnace gas 155 lbs. (.All pressures are absolute.) . 

Fuel Confuinption \Ch) per B.Il.P. Hour, and actual thermal 

efficiencies ( r iw). 


Coal gas, cu. ft. 

Producer gas, 

Blast-furnace gas, 
Coke-oven gas, 

Gasoline, lb ( s - 

Kerosene, 

Alcohol, 90% 
Petroleum, crude, 
(Diesel motors) 


5 H. 

P. 


25 H.P. 

100 

HP. 

c h 

Vw 

Ch 

Vw 

Ch 

Vw 

19 

0 . 

20 

15.5 

0.24 

13.8 

0.27 

105 to 

0 , 

.17 

85 to 

0.21 

75 to 

0.24 

115 



92 


80 

0.24 



115 

0.20 

100 




30 

0.19 

24.7 

0.23 

0.66 

0 

.19 

0.55 

0.23 



1 .2 

0 . 

.11 

1.02 

0.13 



1 .1 

0 

.22 

0.92 

0.26 


0,315 

0.55 

0 

.25 

0,51 

0.27 

0,44 













INTERNAL-COMBUSTION ENGINES. 


97 


Properties of Fuels. 


Coal-gas, average. . . 

“ N. Y. City. 
Producer-gas. 
Anthracite. 


Coke. 

Water-gas (coke). 
Blast-furnace gas. 
Coke-oven gas. .. . 

Natural gas. 

do. Pittsburgh . 
* Acetylene. 


Petroleum. 

(Kerosene). 

Benzine, gasoline. . . 
Alcohol, grain (90%) 
wood. 


B.T.U. 
per Cu. Ft. 
(H.) 

Lbs. per 
Cu. Ft. 
(Atmos. 

Cu. Ft. 
per Lb. 
Pressure.) 

650 

.035 

28.5 

710 to 720 



140 

.062 

16 


to 

to 

130 

.075 

13.5 

275 

.044 

22.7 

106 

.08 

12.4 

450 

.042 

24 

1,000 to 1,100 

.0458 

21.83 

495 to 585 



1,550 



B.T.U. per Lb. 



18,500 

50 

.02 ) 

22,000 



18,000-20,000 

43.8 

.0229 J 

10,900 

51.9 

.019 

8,300 




Cu. Ft. Air Re¬ 
quired for Com¬ 
bustion of 1 Cu. Ft. 
Gas. 

Theoret. Actual. 


5.6 to 6.5 


. 85 
to 

1 

2.4 

.75 

5.3 

9 


12.5 


9 to 10 


1.1 
to 
1.4 
3 to 4 
1 to 1.2 
7 

12.5 
18 to 20 


Cu. Ft. Air per Lb. 
Fuel. 


185 

96 


( 


250 to 350 

240 to 320 
125 to 190 


* One pound of calcium carbide liberates 5.75 cu. ft. of acetylene gas. 

Cooling Water (when entering cylinder jacket at about 60° F. and 
leaving at about 150° F.) should be supplied at the rate of 40 to 45 lbs. 
per hour per I.ll.P. (or 5 to 5.5 gal.). Supply tanks should have a capac¬ 
ity of 20 to 30 gal. per I.H.P. 

Efficiencies. Actual thermal efficiency, ijw = 2,545 -i-HOh. Mechanical 
efficiency, >?m = B.H.P.-hI.II.P. Indicated thermal efficiency, >?< = r t w - 5 -)? m . 
Theoretical thermal efficiency, r /< = ( 1.25 to 2)iji. 

Average Values of vm (Lucke). 


I.H.P. of Engine. 

500 and larger.. . 

25 to 500. 

4 “ 25. 


Four-cycle. 

.81 to .86 
.79 “ .81 
.74 “ .80 


Two-cycle. 

. 63 to . 70 
.64 “ .66 
.63 “ .70 


Brake Horse-Power ^aspmymE (12 X33,000) = (xd 2 sE x 65X0.85)-*- 
(4 X 12 X33,000) =0.0001096d 2 s/?, where a = area of cylinder in sq.in.= 
0.7854d 2 , s = stroke in inches, p m = mean effective pressure (average = 65 lbs. 
per sq. in.), Tjm = .S5, E = number of explosions per min. = r.p.m.A- 2, for a 
four-cycle engine. 

Piston Speeds. Average practice in ft. per min. = 600 +0.2 X H.P. 

Valve Setting. The exhaust should close when engine is on center; 
the inlet should open about 5 ° after center is passed and continue about 
10° beyond center after compression has begun. 

Ratio of Clearance to Stroke (-^-), where c = volume of clearance 
space in cu. in.-*-area of cyl. in sq. in. 


Natural gas. . .. 

Rich gas, rich mixture. 

“ “ , lean “ . 

Lean gas. 

Benzine. 

“ (Banki). 

Petroleum, Alcohol. 

(Diesel) 


c-v-s. Compression. 


0 

3 



100 

lb. 

per sq. 

in 

0 

47 

to 0.77 

65 to 

40 


4 4 

0 

26 

“ 0.38 

115 “ 

80 

4 » 

4 4 4 4 

4 4 

0 

18 

“ 0.26 

170 “ 

1 15 

4 ‘ 

4 4 *4 

4 4 

0 

54 

“ 1.44 

56 “ 

28 

4 4 

4 4 4 * 

4 4 

0 

146 

“ 0.177 

210 “ 

170 

i i 

4 4 4 4 

4 « 

0 

42 

“ 0.77 

70 “ 

42 

4 t 


4 4 

0 

072 

“ 0,077 

500 “ 

450 


4 * M 

4 S 


























































98 


HEAT AND THE STEAM ENGINE. 


Expansion and Compression Laws. PV n =P\Y\ n . For expansion n 
ranges from 1.25 to 1.4, and for compression, from 1.2 to 1.5. For expan¬ 
sion, n is generally taken at 1.35, and at 1.3 for compression. If n is taken 
at 1.33, the following formulas may be used: 

Pressures and Temperatures (Absolute). Let P = suction pressure 
in lbs. per sq. in., P c = compression pressure, Pe = explosion pressure, P r = 
exhaust pressure, T = initial iemperature of charge in degs. F. absolute, 
T r = temp, at end of compression, Te = explosion temperature, T r = exhaust 
temperature, s = stroke in in., and c = clearance expressed as inches of 

stroke. Then, P c = P^/ [7^+c) -*■ c ] 4 - T for scavenging engines = 100 ( 1+ ~) 

+ 461; for ^on-scavenging engin es , T — 120[1 + (c-s-s)] + 461. 

T c = T*^/P c + P= T^/ [(s + c) -h cl. Te = T c + R if scavenging; if not, T e 
= P c + P-h[ 1 + (c-^-s)], where R is the rise of temperature due to explosion 
and is obtained from a table which follows. Pe = P c Te+T c . P r = 


• ' / 4 

p e ^- ’y , where scinches of stroke completed at point of release. 

Tr = Te P7+Pr = Te + ^/[(Si + c) H- c]. 

Ratio of Air to Gas (volumetric), a = (C-f- 50) ; 1 for best economy, 
a = ((7-e-60) ’ 1 for maximum possible load. C = calorific value of gas in 
B.T.U. per cu. ft. 

Calorific Value of Explosive, Mixture, Ci = G-Ka+l). 


Properties of tlie Constituent Elements of Gases. 

(32° F., atmospheric pressure.) 



Specific 


Heat. 


k v - 


Hydrogen, H. 

2.414 

3.405 

Marsh-gas, CH 4 . 

.470 

.593 

Ethylene, CoH 4 . 

.332 

.404 

Carbon-monoxide, CO. 

. 176 

. 248 

Carbon-dioxide, C0 2 . 

.154 

.217 

Nitrogen, N. 

.173 

.244 

Oxygen, 0. 

A j r . 

. 156 
. 169 

.218 

.2377 

Gas - engine exhaust 



(coal gas).... 

.189 

.258 



Lbs. 

Oxy¬ 

gen 

Cu. ft. 
Air re¬ 
quired 
by 1 
cu. ft. 
of Gas 
for 

B.T.U. per lb. 
of Constituent 

Lbs. . 
per 
cu. ft. 

per lb. 
Gas 
for 
Com- 

Gas. 


Com¬ 

bus¬ 

tion. 

High. 

Low. 

bus- 

tion. 

.00559 

8 

2.43 

61,560 

51,840 

. 0445 

4 

9.66 

23,832 

21,438 

.0778 

3.434 

14.A. 

21,384 

20,016 

.0777 

.571 

2.41 v 

4,392 

4,392 

. 1221 
.0778 



B.T.U. per 

.0888 



cu. 

ft. 

.08011 



High. 

Low. 



H 

344.12 

289.79 



CH„ 

1060.52 

954 



c..h 4 

1663.68 

1557.24 



CO 

341.26 

341.26 


(Weights in above table have been calculated from the latest values 
given to atomic weights. The B.T.U. values have been taken from Des 
Ingenieurs Taschenbucli. The values for specific heat are taken from a 
table by W. W. Pullen, in Fowler’s Pocket-Book.) 

Calculation of the Calorific Value of a Gas (1 cu. ft. at 32° F.). 
The table on page 99 gives the calculations for a high-grade coal-gas. 

The difference between the high and low values of the B.T.U. in the 
tables is due to the heat of condensation of that amount of steam which 
results from burning the hydrogen in one cubic foot of gas. The low 
vah’e should be used in calculations, this being the only heat liberated 
in the cylinder. 







































INTERNAL-COMBUSTION ENGINES. 


99 



Volume 
in cu. ft. 

Weight 
in lbs. 

Specific Heat. 

k . 


II. 

CIL. 

c 2 h 4 . . . . 

CO. 

COo. 

n. :.. . . 

.3978 
.4516 
. 0638 
.0704 
.0108 
. 0050 

.00222 
.02010 
.00496 
.00547 
.00132 
.00039 

. 1553 
.2738 
.0477 
.0278 
.0059 
.0020 

.2191 
. 3455 
.0580 
.0392 
. 0083 
. 0003 

1.0000 

.03451 

.5127 

.6732 


B.T.U. 
(Low). 


115.28 
430.83 
99.35 
24.02 

669.48 


Air, cu. 
ft. for 
complete 
Combus¬ 
tion. 

.967 
4.362 
.925 
. 170 

6.424 


kp-hkv = 1.313 = n. 

.inns 

t-JiW 1 S' 07596 S SpecWc' 

F - n t IT ^T 4 ' ir Heat required to raise one cubic foot 1 degree 

t F ur7=°K2 B B T f U U."A/. H Fir-t3l4- by F C S bUSU ° n 1 

mined to* hS"^ folio°^ bU5,i0n ° f C ° a ‘- gaS h “ ^ ewimentally deter- 


Ratio of mixture. 6:1 

Efficiency, x . _465 


8 1 10 : 1 12 . 1 

.543 .575 .580 

inThl r ^-1S7l r x M 57 r 5-“5 t 15" e F P ' OSi ° n C ° n5tant voIume ’ *-«*+*. 

If this mixture be compressed from 15 lbs. absolute to 80 lbs absolute 
in a common or non-scavenging engine, (s 4-c) -*-c = 3.51, s = 2 51c 
s . c — -.51, and c-ks = .4. Substituting these values in the Drecedim? 
formulas. 7 7 = 629° F„ 7^ = 956° F., Tr = 2 753° F r = 1 860° F p J 
15 }b., Pc = 80 lb., P e = 231 lb., P r = 47.86 lb.’ (*, taken = 0.9sf 
hor a scai-enging engine, P = 601° F., 7’ r = 914° F 7V = 3 49q°p 

Z-2WF. Pe -300 lb.. 0-62.3 lb. (AH pressure.; iZd temped 
tures are -absolute.) 

The Diesel Engine. Clearance = 0.0625 to 0.07 Xvol. of cvl. Com¬ 
pression. PVy = C; expansion: PV^ = C. Temperature at the end of 
compression to oOO lbs. pressure = 720° F. ; temoerature at the end of 
combustion = 1,922° F. A test by Mr. Ade Clark in March, ’03 showed 
a consumption of 0.333 lb. of Texas fuel oil (19,300 B.T.U. per lb ) oer 
I.H.P., or 0.408 lb. per B.H.P. and an efficiency of 32.3% 

V arious Engine Performances. Ivoertir.g engine, 900 II P 28% 
efficiency on B.H.P. (33.5% eff. I.H.P.). A Diesel engine of 160 H P 
tested by W. H. Booth used 0.45 lb. of heavy fuel oil per B II P \ Crosslev 
engine using producer-gas required -from 0.65 to 0.85 lb. anthracite “per 
c 1 , 5; Hornsby-Akro.vd oil engine showed a consumption of 0 785 lb 

of crude Texas oil per B.H.P. 

Design and Proportions of Parts. The following matter is condensed 
from an article by S. A. Moss, Ph. I)., in Am. Mach., 4-14-04. The 
results have been derived from 76 single-acting engines (5 to 100 H.P.) 
made by 20 builders and \yi 11 serve as an index of average practice Maxi¬ 
mum exnlosion pressures varied from 250 to 350 lbs. per sq. in and 300 
lbs. has been taken as an average. Compression varied from 50 to 100 
lbs. (50 for gasoline, 100 for natural gas) and 70 lbs. has been taken as 
an average. Maximum H.P. was found to be about 1 125Xrated II P 
Mechanical efficiency about 80%. Values to the right, in brackets, are 
taken from Roberts Gas-Engine Handbook. 


Diam. of cylinder in ins. 

Thickness of cylinder wall, t. 

“ jacket “ 

‘ ‘ water jacket... 


= d. 
d 

= ^+0.25 in. [£ = 0.09d]. 


L0F C, 


16 
= 0 . 6 £ 
= 1.25* 


[£ = 0.045(1]. 
[£=0.1d] 




































100 


HEAT AND THE STEAM ENGINE. 


No. of cylinder-head studs.= 0.66d + 2. 

External diam. of studs.= d = 12 (average). 

Length of stroke l. .= 1.5d 

“ “ connecting-rod, c.= 2.5 1 

Weight of piston, w in lbs.=1.3 a (a = area of cyl. in sq. in.). 

“ “ connecting-rod n\ .=0.8a. 

“ “ reciprocating parts (w + 0.5«>i). = w?a ; w 2 average = 1.7. 

Length of piston trunk..= 1.5d (average). 

Bearing pressure on piston due to weight =0.89 lb. per sq. in. 

Thickness of rear wall of piston.= d=10. 

Wrist-pin, diam .= 0.22d; length = 1.75Xdiam. 

Diam. at mid-section of connecting-rod . = 0.23d. 

Crank-pin: length = 0.39d; diam. = 0.41d. 

Crank-throws: thickness = 0.26d; breadth = 0.55d. 

Diam. of crank-shaft, s = 0.375d. 

Main bearing, length = 0.85d (bearing pressure averages 125 lbs. per sq. in.). 

Fly-wheel - outside diam.= 12 1 30O-=-A / ’(N = r.p.m.). 

“ weight in lbs.=33,000XjLP. -i-N. 

Revs, per min. N .=800 = v / /[W = 380-5-(B.H.P.) 0 - 21 for 4-cycle, 

increase £ for 2-cycle.] 

Piston speed, ft. per min. . . . = 133 
Exhaust pipe diam.=0.28d. 


valve 

Inlet 
Gas pipe 
‘ ‘ valve 
Air pipe 
Max. B.H.P. = d 2 ZV14,400. 
by 13,500 (2-cycle).] 


= 0.3d [0.35d], 

= 0.27d [0.316d]. 

= 0. lid. 

= 0.15d. 

= 0.25 d 

[For gasoline, divide by 


18,000 (4-cycle) or 


M.E.P. = 50 to 85 lbs. per sq. in. 


Speed of exhaust gases = 5,200 ft 

“ inlet charge . =6,400 “ 

“ “gas .=3,700 “ 

“ “ air .=6,900 “ 


average, 70 lbs. 

per min. (average). 


Dr. Lucke (in “Gas-Engine Design,” D. Van Nostrand Co.) states that 
engines should be designed to withstand max. pressures of 450 lbs. per 
sq. in The following additional formulas are taken from his work. 

Thickness of cylinder wall, Z = (.062 to .075)d-(-0.3 in. Wrist-pin: 
diam.=0.35d, length = 0.6d. 

Piston rings' number = 3 to 10, width = 0.25 to 0.75 in., greatest radial 
depth =0.02d + 0.078 in. (Guklner), or, = 0.033d+ 0.125 in. (Kent). Valve 
diam., v = (0.3 to 0.45)d; valve-stem diam. = (0.22 to 0.3)u; valve lift = 
(0.05 to 0-1 )t> for flat valves,—50% greater for 45° conical valves; valve- 
seats, width = (0.05 to 0.1)i>; valve-faces = (1.1 to 1.5)Xwidth of seat, 
for conical valves. 

The following additional data are taken from E. W. Roberts’ Gas-Engine 
Handbook Z(for two-cycle) = d to 1.25d; diam. of water-pipes = 0.15d; 
diam. of fly-wheel hub = 2s; hub length = 1.75s to 2.25s; mean width 
of oval spoke or arm = 0.8s to 1.2s; mean thickness of arm = (0.4 to 0.5) X 
mean width; number of spokes = 6 (generally). 

Engine Foundations. In order to absorb the vibrations of an engine 

it should be bolted to a foundation whose weight F is not less than 0.21 E^N, 
where E = wt. of engine in lbs. Brick foundations weigh about 112 lbs. 
per cu. ft. and those of concrete about 137 lbs., an average being about 
125 lbs. per cu. ft. Number cu. ft. in foundation = F -s- 125. The inclination 
or “batter” of the foundation walls from top to bottom should be from 
3 to 4 in. per foot of height (E. W Roberts). 


AIR. 

Air is a mechanical mixture of oxygen and nitrogen,—21 parts oyxgen + 
79 parts nitrogen, by volume (23 parts 0 + 77 parts N, by weight). 

1 cu. ft. of pure air at 32° F. and at a barometric pressure ( B ) of 29.92 
inches of mercury (14.7 lbs. per sq. in.) weighs 0.080728 lb., and the vol¬ 
ume of 1 lb, = 12.387 cu. ft. At any other temperature and pressure, 
























AIR. 


101 


weight pel* cu. ft., w — where B = height of mercury 

in barometer in in., t = temperature in degs. F., 1.3.302 = weight in lbs. 

, 4o,l cu. ft. of air at 0° F. and 1 in. barometric pressure. Air expands 
493 of its volume for each increase of 1° F., and the volume varies inversely 
as the pressure. 

Air liquefies at —220° F. (its critical temperature) under a pressure of 
573 lbs. per sq. in. and boils at —312° F. Specific gravity at — 312° F. 
= 0.94. ^Latent. heat = 123 to 144 B.T.U. per lb. Liquid air occupies 
about Boas of the volume of the same weight of free air at normal tem¬ 
peratures. 

Barometric Determination of Altitudes. Pressure of the atmos¬ 
phere at sea-level (32° F.) = 14.7 lbs. per sq. in. Difference of levels (at 

32° F.) in feet = 60,463.4 log — (1), where B and B x are the barometric 

readings of the two levels. If B is taken at sea-level it is equal to 29.92 in. 

29 92 

and Height above sea-level = 60,463.4 log —1 — (2). 

Jd i 

For any other temperatures, t (for B) and t\ (for B j), formulas (1) and 
(2), must be multiplied by a correction factor, c= 1 4-0.00102(t-Hj — 64). 

Approximately, the pressure decreases 0.5 lb. per sq. in. for each thou¬ 
sand feet of ascent. 


Flow of Air in Pipes. Q, in cu. ft. per min. = cS /-where p = differ- 

wL 

ence between the entering and leaving gauge pressures in lbs. per sq. in., 
ci = diam. of pipe in in., L = length of pipe in feet, and w = density of the 
entering air (lbs. per cu. ft.). 


When d — 1 in. 

2 in. 

3 in. 

4 in. 

9 in. 

12 in. 

c = 45.3 

52.6 

56.5 

58 

61 

62 

Richards' formula is 

Q = 100 

,V-if. 




When d— 1 in. 

2 in. 

3 in. 

4 in. 

8 in. 

12 in. 

a = 0.35 

0.565 

0.73 

0.84 

1.125 

1.26 

Flow of Air through Orifices. 

Theoretical velocity in feet per sec. 


v = \ 2*7X27,816^1 —^ 7 ) = 1,337.74^1 — where p is the pressure in the 


reservoir out of which the air flows, and Pi the pressure of the receiving- 
reservoir. For the actual efflux the value of v must be multiplied by 
the proper one of the following coefficients 


Pressure (in atmospheres). 0.1 0.5 1 5 10 100 


Orifice in thin plate. 0.64 0.57 0.54 0.45 0.436 0.423 

“ .short tube. 0.82 0.71 0.67 0.53 0.51 0.487 


Loss of pressure. p = 0.107 vhvL c 2 d, where w at ordinary temps. = 
0.03(pi-r-14.7) 0 ' 71 , P\ (at entrance, absolute) and p both in lbs. per sq. in. 


COMPRESSED AIR. 

Free air is that at atmospheric pressure and at ordinary temperatures 
(14.7 lb. per sq. in., 62° F.). Absolute pressure = gauge pressure-!- 14.7 
lb. Absolute temperature =461° F.-(-reading of thermometer in degs. F. 

Relations between Temperature, Volume, and Pressure. 

p _/F,\ 141 ._ /r f__ /Pi\°- 71 _ /lA 2-44 . i__ /ZiV 41 - /p_\ 0,29 
Pl \V ) W ’ Vi Vp/ U ’ Tj VW \p x ) 

PV = Rz\ i? = 53.354; P = ap. In the foregoing p, V, r, and p,, V lt 
tj are the respective initial and final absolute pressures, volumes, and 
absolute temperatures. 

Work of Compression. Ft.-lbs. of work required to compress 1 cu. 

Pi 

ft. of free air to any desired pressure, Pi, isothermally = 144pXloge —. 












102 


HEAT AND THE STEAM ENGINE. 


r), , 

If y>=14.7 lb., work in H.P. =0.0641 when compressed in 1 mm. 

Ft.-lbs. of work required to compress 1 lb. of free air adiabatically at 
the absolute temperature r, = (ti — r) X778 X0.2375 = 184.7(r x — t) ft.-lbs. 

— lj, where r x is the temp, corresponding to the 

volume to which the air is compressed. For work to compress 1 cu. ft. 
divide above value by the number of cu. ft. in 1 lb. at t. 

In practice the actual work = work of isothermal compression + about 
60% of the difference between isothermal and adiabatic work. 

The Output of a Compressor at any Altitude expressed in per 
cent = 100 — 0.0028 X height in feet (approx.). 

Loss by Cooling varies from 70% under bad conditions to 20% with 
reheating and air injection. 

Loss by Pipe Friction per mile = 5%. 

Reheating. Gain by reheating in per cent = 100 (1-), where t 

V Tx 7 

and ti are the absolute temperatures before and after heating. 

Tests made at Cornell University show that from 28 to 38% gain in 
thermal economy can be made by reheating air from 90° to 320° F., the 
efficiency of the reheater being 50%. There is no additional gain made 
by heating above 450° and if 300° is much exceeded there is danger of 
charring the lubricant. 

Pneumatic Tools (cu. ft. of free air required per min., 80 lbs. pressure). 
Chipping and calking tools, 11 (light) to 17 (heavy); riveting tools, 15 
(+ in. rivet) to 22 (1| in. rivet); drills (metal), 15 (1 in.) to 35 (3 in.); 
wood-boring, 12 (1 in.) to 18 (2£ in.). 



I 


FANS AND BLOWERS. 

Let /t = pressure generated in inches of water (1 in. water = 0.577 oz. 
per sq. in. 1 oz per sq. in. = 1.73 in. water); v = peripheral velocity of 
wheel in ft. per sec.; v\ = velocity of air entering the wheel through the 
suction openings in side of case (25 to 33 ft. per sec.); d = diam. of suction 

openings in in. (for openings on bo th sid es of wheel, d= 13.54v / g-r-2i> 1 ; 

for opening one side only, d= 13.54V / g-Hv 1 ); Z>x = inner diam. of wheel = d 
to 1.5 d; D = outer diam. = 2D X for suction-fans (=3 D x for blowers); 
N = r.p.m. = 229v + D; 6 = width of vanes at D x = 0.25d to 0.4g? for suction 
opening on one side ( =0.5 d to 0.8d for openings on both sides); 6 X = width 
of vanes at D, = bD x -+ D] No. of vanes = 0.3757); q — cu. ft. of air per 
sec.; t) = efficiency = 0.5 to 0.7 for large fans (0.3 to 0.5 for small fans); 
c=1.2 to 1.4 for large fans (1.4 to 1.7 for small fans); a = angle which the 
extreme outer element of a vane makes w ith the radius at that point. 

Then, i; = 3.28[4 tan « + v / (4 tan «) 2 + 200/i]. a is positive when the vanes 
are curved or inclined backward from the direction of rotation (negative 
when forward). For radial vanes o =0, and v = 46.4cV / / i , = 4G.4\// i = q. 
Area of discharge-opening in sq. in. = 144 q- j-t> 2 , where i> 2 = velocity of air 
in pipe in ft. per sec. H.P. required = qh+ 105.7>?. Outer diam. of disc 
fan in in. =3 V ' , </; i) = 0.2 to 0.3. 


MECHANICAL REFRIGERATION. 

Mechanical refrigeration is produced by expanding a heat medium 
from a normal temperature to one which is below the usual limits for 
the climate and zone where the expansion takes place. Media are chosen 
with regard to their willingness to surrender their heat energy to surround¬ 
ing objects, and vapors are therefore best employed. 

The vapor chosen is compressed and then relieved of its heat in order 
to diminish its volume. It is then expanded so as to do mechanical work 
and its temperature is lowered. The absorption of heat at this stage by 
the vapor in resuming its original condition constitutes the refrigerating 
effect. 












MECHANICAL REFRIGERATION. 


103 


? ulphur dioxide (S0 2 ), Pictet fluid (SOo + 3% of car¬ 
bonic acid, C0 2 ) and air are most employed, ammonia and air being of 

wuui'd'be‘SSectiSSble “ USed °" shipboard where 

AS /Fix 0 - 41 _ (V \ 0 - 29 T 

Air. ^ _ \P]/ —is cheap and harmless, but its use 

° n accoui R ,°f its bulk and the size of the machinery employed 
mo o e R C m measured in ice-melting effect (latent heat of fusion of ice = 
f,, , B1 V-) ia between 3 and 4 lbs. of ice-melting capacity per lb. of 

fuel, assuming 3 lbs. of fuel per H.P. 

Saturated Ammonia is inexpensive, remains liquid under atmospheric 
pressure only below —30 F., and at 70° F. under 115 lbs. gauge pressure. 


Properties of Saturated Ammonia. 


Temp. 
Degs. F. 

Abs. Pres¬ 
sure, Lbs. 
per Sq. In. 

Heat of 
Vaporization, 
B.T.U. 

Vol. of 
Vapor. 
Cu. Ft. per 
Lb. 

Vol. of 
Liquid. 
Cu. Ft. per 
Lb. 

Wt. in Lbs. 
of 1 Cu. Ft. 
of Vapor. 

-40 

10.69 

579.67 

24.38 

0.0234 

0.0411 

— 30 

14.13 

573.69 

18.67 

.0237 

.0535 

— 20 

18.45 

567.67 

14.48 

.0240 

. 0690 

—10 

23.77 

561.61 

11.36 

.0243 

. 0880 

0 

30.37 

555.5 

9.14 

. 0246 

. 1094 

f 10 

38.55 

549.35 

7.20 

.0249 

1381 

20 

47.95 

543.15 

5.82 

.0252 

1721 

30 

59.41 

536.92 

4.73 

.0254 

2111 

40 

73 

530.63 

3.88 

.0257 

.2577 

50 

88.96 

524.30 

3.21 

.0261 

3115 

60 

107.60 

517.93 

2.67 

. 0265 

3745 

70 

129.21 

511.52 

2.24 

.0268 

4664 

80 

154.11 

504.66 

1.89 

.0272 

.5291 

90 

182.8 

498.11 

1.61 

.0274 

.6211 

100 

215.14 

491.5 

1.36 

.0277 

.7353 


Ammonia Compression System. T^e ammonia vapor is compressed 
to about 150 lb. pressure and a temp, or 70° F., and is then allowed to 
flow into a cooler or surface-condenser, where the heat due to the work 
of compression is withdrawn by the circulating water and the vapor is 
condensed to a liquid. It is then allowed to pass through an expansion 
cock and to expand in the piping, thereby withdrawing heat from the 

brine with which the pipes are surrounded. This brine is then circu¬ 
lated by pumps through coils of piping and produces the refrigerating 
effect. The expanded ammonia-gas is then drawn into the compressor 
under a suction of from 5 to 20 lbs., thus completing the cycle of operath ns. 

The brine consists of a solution of salt in water. Liverpool salt solution 
weighing 73 lbs. per cu. ft. (sp. g. = 1.17) will not congeal at 0° F. Amer¬ 
ican salt brines of the same proportions congeal at 20° F. Ammonia 
required = 0.3 lb. per foot of piping. Leakage and waste amount to about 
2 lb. per year per daily ice capacity of one ton. The brine should be about 
6° colder than the space it cools. 

Ammonia Absorption System. In this system the compressor is 
replaced by a vessel, called the absorber,—where the expanded vapor 
takes advantage of the property of water or a weak ammoniacal liquor 
to dissolve ammonia-gas. (At 59° F. water absorbs 727 times its own 
volume of ammonia-vapor.) The liquor in the absorber is then pumped 
into a still heated by steam-pipes, where the ammonia-gas is*vaporized, 
the remainder of the process being then the same as in the compression 
system. The absorption system is less expensive to install, and com¬ 
mercial ammonia hydrate (62% water, sp. g. =0.88) may be used in the 
absorber. 

Efficiency. Ice-melting capacity per lb. of fuel =wst-i- 142.2tc,; Ice¬ 
melting capacity in tons (2,000 lbs.) per day of 24 hours = 24vst + 
(142.2X2.000), where w = lbs. of brine or other fluid circulated per hour 






















104 


HEAT AND THE STEAM ENGINE. 


it', = lbs. of fuel used per hour, s = specific heat of the circulating fluid, 
and t = range of temperature experienced by the circulating fluid 1 deg. . . 

Design of a Compression Machine. The weight of the medium 
required is determined by the condition that each pound must withdraw 
from the brine the heat necessary to change the liquid medium in the 
condenser at t (with a heat of liquid in each lb. =h) into saturated vapor 
at U in the vaporizer, where the total heat of evaporation per lb. n. ine 
heat withdrawn per lb. per min., L = If — h, and, in ice made Pe r hour, 
the weight of the medium, w = 142.2Xlbs. of ice made per hour -r-60(/f hh 
Assuming the compression to be adiabatic, the absolute^ temperatu e 

of the superheated vapor leaving the cylinder, T s = T 2 (j^) . where T 2 

is the absolute temperature (degs. F.) of the vapor in the expansion or 
vaporizer coils in the brine, and pi, p 2 are the pressures before and alter 

6 X The 8 cooling water required in the condenser, W = u{k P (ts - ty) + H — h] lbs., 
where k P = specific heat of the superheated vapor at constant pressure, 
ts and h = temperatures (F.) of the compression cylinder and condense 
respectively, and (H — /i)=heat of vaporization at the pressure Pi o c 

denser. , . . , 

The H.P. of the steam cylinder driving the compressor 


778w 

33,000 


[k P (ts — tj ) + Hi — H 2 ], 


where //, and Ho are the total heats of vaporization at the pressures and 
temperatures in the condenser and vaporizer, respectively. I his value 
must be increased to allow for heat and friction losses. 

, wX vol. of 1 lb. of vapor 

The volume of the compressor cylinder- Nq ^ strokea per m i n . ' 

Specific Heats at Constant Pressure (k P ). Ammonia, 0.508; car¬ 
bonic acid, 0.217; sulphur dioxide, 0.1544. 

Temperatures for Cold Storage. Fruits, vegetables, eggs, brewery 
work, 34° F.; butter, cheese, shell oysters, 33° ; dried fish, canned goods, 
35°; flour, 40°. The following should be frozen at the first temperature 
and then maintained at the second: Butter, 20°, 23°; poultry, -0 , 30 , 
fresh fish, 25°, 30°; tub oysters, 25°; fresh meat, 25°. 


HEATING AND VENTILATION. 

Ventilation. Impurities in air are due to carbonic acid and organic 
particles exhaled from the lungs, water vapor from nerspiration, dust, 
smoke noxious gases, etc. The measure of impurity, however, is taken 
as the content of carbonic acid, which should not exceed 6 to 8 parts in 
10 000 Fresh air contains 4 parts (country air, 3 to 3.5) in 10,000. itie 
hourly yield of C0 2 per person is 0.6 cu. ft.; consequently each 1,000 cu. 
ft of fresh air can take up at least 0.2 cu. ft. of C0 2 and not exceed the 
limit of 6 parts in 10,000; hence 3,000 cu. ft. of fresh air per person, if 
uniformly diffused, will keep the respiratory C0 2 down to that limit. It 
is further found that the atmospheric contents of a room may be changed 
three times per hour without causing inconvenient draft, hence 1,000 
cu. ft. of air space is a proper provision per person. From 2,000 to 2,o00 
cu ft. per person per hour is sufficient for auditoriums used but tor two 
or three hours at a time. School-rooms should have at least 1,800 cu. ft. 
per scholar per hour, and in hospitals from 4,000 to 6,000 cu. ft. per patient 
per hour should be supplied on account of the various unhealthy excre- 

According to Rietschel (Ing. Taschenbuch) the hourly supply of air per 
capita in cubic feet should be as follows: Hospitals, adults, ..,600, chil¬ 
dren 1,200? schools, pupils under 10 yrs., 400 to 600,—pupils oyer 10 yrs., 
600 to 1,000; auditoriums, 600 to 1,100; work rooms, 600 to 1,100; living 
rooms, 1 to 2 times cubic contents; kitchens and closets, 3 to 5 times 

cubic contents. . , , , , 

Carpenter states that the number of changes of air per hour should be 
as follows Residences,—halls, 3; living rooms, 2; sleeping rooms, 1. 
Stores and offices, 1st floor, 2 to 3; upper floors, 1.5 to 2. Assembly 
looms, 2 to 2.5. 

















heating and ventilation. 


105 


Heating of Buildings. Let- IF = sq. ft. of transmitting surface, fi = 
inside temperature, <2 = outside temperature, both in degs. F. t = li~t 2 , 
« = a coefficient representing for various building materials the heat loss 
r j. r ^ nsmisslon P er S Q- ft- of surface in B.T.U. per hour for each degree 
of difference of temperature on the two sides of the material, and H = 
the total heat transmission = Wkt. 

Values of k (Ing. Taschenbuch). 

Thickness of wall in 


. inches. 4 8 12 16 20 24 28 32 36 40 48 

for brick. 0.53 .38 .30 .25 .22 .19 .17 .15 13 .12 

Do. sandstone. 0.45 .39 .35 .32 .29 .26 .24 22 19 


For limestone add 10% to values for sandstone. 

Solid plaster partitions: 1.75 to 2.25 in. thick, 0.6; 2.5 to 3.25 in., 0.48 

rloors; joists with double floors, 0.07; stone floor on arches, 0.2; planks 
laid on earth, 0.16; planks on asphalt, 0.2; arch with air-space, 0.09- 
stones laid on earth, 0.08. 

Ceilings: joists with single floors, 0.1; arches with air-space, 0.14. 

Windows: single, 1.00; double, 0.46. 

Skylights: single, 1.06; double, 0.48. 

Doors, 0.4. 

The above values should be increased according to conditions as follows: 
For rooms unusually exposed, add 5%; for N., NE., E., NW. and W. 
exposures and where height of ceiling ( h ) exceeds 18 ft., add 10%; for 
& = 13 ft., add 3^%; for h = 15 ft., add 6|%. 

For rooms heated daily, but not at night, add A =0.0625 (N-l)H-t-Z; 
and for rooms not heated every day, add B = 0.1(8 + Z)H = where N = 
No. of hours between cessation of heating and restarting of fire, and Z = 
No. of hours from starting of fire until rooms attain required temperature. 

In heating assembly rooms account must be taken of the heat given 
out by audiences and illuminants. A person gives out about 400 B.T.U. 
per hour, an ordinary gas-burner about 4,800 B.T.U. per hour, and an 
incandescent electric lamp (16 c. p.) 1,600 B.T.U. per hour. A gas-burner 
vitiates the air as much as 5£ persons. 

B. T. U. per Hour required to Heat a Room. (Carpenter.) No. of 

/ y\,(^ \ 

B.T.U. = + G + J t, where n = No. of changes of air per hour, C = 


cu. ft. in room, G = sq. ft. of glass, TF = sq. ft. of -wall surface exposed 
to outside air, and t = difference between inside and outside temperatures in 
degs. F. 

Radiation. Ordinary bronzed cast-iron direct radiators give out 
about 250 B.T.U. per hour per sq. ft. of radiating surface, with steam 
of 3 to 5 lbs. pressure. Unpainted radiating surfaces of the ordinary in¬ 
direct type give out about 400 B.T.U. per sq. ft. per hour. For hot-water 
heating 60% of these values may be taken. 

Hot-air furnace walls transmit about 500 B.T.U. per sq. ft. per hour if 
the walls are much extended, and about 800 B.T.U. if the surfaces are 
smooth, air temperatures at registers being from 100° to 150° F. Boilers 
when coal-fired will transmit 2,500 to 4,000 B.T.U. per sq. ft. of heating 
surface per hour, and from 4,000 to 5,000 B.T.U. when coke-fired. Hot¬ 
air systems provided with blowers yield transmission values up to 2,000 
B.T.U. per sq. ft. per hour. 

Approximate Heating Values of Radiating Surfaces. One square 
foot of radiating surface will heat by direct steam radiation: Dwellings, 
school-rooms, offices, 60 to 80 cu. ft.; halls, lofts, stores, factories, 75 to 
100 cu. ft.; churches, large auditoriums, 150 to 200 cu. ft. For direct 
high-temperature hot-water heating, take § of above values,—for low- 
temp. hot-water heating, take % of same. For indirect radiation, take $ 
of the value for direct radiation. 

Sizes of Pipes for Steam-Heating. (Wolff.) Allow 0.375 sq. in. 
sectional area per 100 sq. ft. of radiating surface for exhaust-steam heat¬ 
ing, 0.19 sq. in. per 100 sq. ft. when live steam is used, ahd 0.09 sq. in. 
per 100 sq. ft. for returns. Each horse-power of boiler capacity will sup¬ 
ply from 80 to 120 sq. ft. of radiating surface. (“Steam.”) In good hot- 
water boilers, the ratio between grate area, boiler heating surface, and 
radiating surface is 1 : 40 . 200. 







HYDRAULICS AND HYDRAULIC 
MACHINERY. 


Water (1 part H + 8 parts O.) 


Degs. F. 

Lbs. per 
cu. ft. 

Relative 

Vol. 

Degs. F. 

Lbs. per 
cu. ft. 

Relative 

Vol. 

32 

39. 1 

50 

60 

62 

70 

80 

90 

62.418 

62.425 

62.41 

62.37 

62.355 
62.31 
62.23 
62.13 

1.00011 

1.00000 
1.00025 

1.00092 
1.00110 
1.00197 
1.00332 
1.00496 

100 

120 

140 

160 

180 

200 

210 

212 

62.02 .. 
61.74 
61.37 

60.98 

60.55 

60.07 
,59.82 
59.76 

1.00686 

1.01138 

1.01678 

1.02306 

1.03023 

1.03819 

1.04246 
1.04332 


For sea-water, multiply above weights by 1.026. 
Pressure Equivalents. 


1 ft. water af39.1° F. (max. density)-62.425 lbs. 

= () 0295 atmospheres on the sq. in. 

1 lb. on the sq. ft. at 39.1° F. = 0.01602 ft. of water; 1 lb. per sq. in. = 2.307 

1 atmosphere ^29.922 in. mercury) = 33.9 ft. of water. 

1 ft of water at 62° F. (normal temp.) = 62.355 lbs. per sq. ft. 
i tt. oi \\ aiei at v. =0.43302 lbs. per\sq. in. 

1 inch of water at 62° F. (normal temp.) = 0.036085 lbs. per sq. in. 

Ilvdrostatic Pressure. The pressure of a liquid against any point of 
anv surface upon which it acts is always perpendicular to the surface at 
that point and, at any given depth, is equal in all directions and due to 
the weight’ of a uniform vertical column of liquid whose horizontal cross- 
section is equal to the area pressed upon and whose height is the veitical 
distan-e from the center of gravity of the surface pressed to the surface 

° When^a'liauid pressure is exerted on one side of a plane area, the result- 
„nt force experienced by the area is perpendicular to the area, equal to 
tlie sum of all the pressures and acts at a definite point called the center 

renters' of Pressure h( = vertical depth from surface of liquid). 

Re” angle: upper side parallel to liquid surface and distance 'u from same, 


h 


\Q/ 9 , 


,+2a 


3' 2 hi + a 


+ hi; if 


, 2a 

h\ = 0, /i =—. 


Triangle: base lying in surface of liquid, h a : 2; 
surface, base horizontal, /i = 3a = 4. 


vertex in liquid 


Circle or Ellipse: h = a + h x + 4(a + ^") ; lf hl °* h 5a : 4 


106 
























hydraulics and hydraulic machinery. 107 


or ™JuSJ , SSiri s ™? i emp^ ght ° f ,riangle ° r rec,an|tle - ratIi,,s of circle 

Buoyancy. When a body is immersed in a liquid it is buoved un bv 

sinking e< Th! t0 the 7 eight of the 1 ic 1 11 • (1 it displaces whether floating or 
Hi,? pressure may be considered as acting at the c of g 

^ spla , ced ll ^ ld - or, as it 1S termed, at the center of buoyancy and 
j Me t lme drawn through the center is called the axis of flotation ’ The 
connecting the center of buoyancy and the c. of g. of a floating body 
at rest is called the axis of equilibrium and is vertical. If an external 
f+h Ctmg +° n body in<dmes the axis of equilibrium, a vertical line 
center he The 61 * ^,q^ ancy - inters l e , cts this axis at a point called the meta- 
nt m 0 / he , eqpillbnum 1S . stable, indifferent, or unstable, according 
above, coincident with or below the center of buoyancy 

nh?re h«l.fnce« ’ and Vel( ? clty Energy. The pressure of the atmos¬ 
phere balances the pressure of a column of water 33.9 ft, high, and the 

head of the column, // = 33.9 =14.696 = 2.307p. If a vertical gauge- 
tube be inserted m a pipe the water will rise in it to a height propor- 
tional to the pressure; then, connecting head and pressure PA =GIIA 

U h ’] +" d f • ’’,7 h % e ^ T supporting pressure in lbs. per sq. ft., 

17 = height of column m ft., G = weight of 1 cu. ft. of water in lbs., and A 

= area of cross-section of column in sq. ft. 

Head and Velocity. A water particle (weight = w) at height, H 
has a potential energy equal to wH, and when it has fallen through H 

its kinetic energy = Neglecting friction and other losses, wH = wv 2 + 2g 

and v = ^2gH = 8.02\//7. 

Any gh en portion of water flowing steadily between two reservoirs 
which are kept at a constant level will,—neglecting friction and viscosity 
—possess an unvarying amount of energy which may be due to head’ 
pressure, velocity, or to all three. If a vertical gauge-tube be inserted 
at any point of the pipe connecting the reservoirs the water will rise in it 
to a level below that of the reservoir from which it flows, a portion of the 
head energy represented by the difference of levels having become kinetic, 

and the total head (77i) consists of H due to unexpended fall+ —due to 

/ V 2 ° 
pressure (as shown by gauge-tube)-!-— due to velocity. 

Multiplying each by w gives the respective energy, the energy of 1 lb. 

of water being 7/* = // + ^* +x~. 

(jt Zg 

By sufficiently contracting the sectional area of the pipe at some point 
between the reservoirs the throttling so caused will reduce the pressure 
below that of the at mosphere and create a partial vacuum. This principle 
is employed in jet-pumps (efficiencies, 30 to 72%). 

Discharge of Water through Orifices. If a reservoir is emptied 
through an orifice near its bottom, the volume of the water passing, 0 = 
velocity Xarea of orifice, and, neglecting resistances, The Theoretical Dis¬ 
charge in cu. ft. per sec. q = Av = 8.02.4 ^H. On account of resistances 
v is reduced, and, letting c x coefficient of velocity, 77 = 8.02 c^H. If 
the reduced velocity be considered as due to a loss of head, 77 r , a coeffi¬ 
cient of resistance, p, may be adopted, H r being taken as equal to pH, 
where 77 x is the remaining or unexpe nded head. 77 = 77 x + H r = 77,+ p h[ 

“=(1 +p)Hi, and v = 8.02v / Z/i= 8.02/^. Also, = V- H 


A = 


/ 


1 


\+o' 


and p = — 7; 

O 2 


- 1 . 


■ +/»* wi ' ~7 r i+p' 

This loss occurs within the vessel and orifice. 


x 1 «/ o | 

A further loss is caused by the contraction of the jet area at a distance 
from the orifice equal to one-half the jet diam. Let k = coefficient of con- 

f TV 

traction; then, Actual Discharge incu.ft. per sec., q a = c x vkA =8.02 kA \ ——- 
or, letting C = c x & = coefficient of discharge, q a = &.02ACv H. 














108 HYDRAULICS AND HYDRAULIC MACHINERY. 


Average Values of Coefficients. 



Orifices. 


Sharp-edged. 

Re-entrant 

Cyl. 

Cylinder. 

Bell-mouthed, 

II II II 11 

0.97 

0.0628 

0.64 

0.62 

1.00 

0 . 

0.53 

0.53 

0.82 

0.487 

1.00 

0.82 

0.99 

0.02 

1.00 

0.99 


Measurements of Water-Flow over Weirs. Let a stream be partly 
dammed and the water allowed to flow through a rectangulsm notch, o 
wet?, which is beveled to sharp edges on the intake side To find^ the 
discharge, divide the head. H (or distance from edge of notch to surfaces of 
water), into small portions, /q.and consider each small rectangle (/qX_tengt 

of notch, L) as a separate orifice. At any depth, J*i, r = 8.02 H l and 
the discharge through the small rectangle = 8.02/>//i. Representing t e 
various discharges by horizontal lines of proportionate length, te g 
bounding these lines will be found to be a parabola of .base - 8X)2i> n, 

and height = head H (the lines'varying in length asVfl,). ™ 
theoretical discharge will then be equal to the area of the parabola, , 
q = 3X8.02L//5 = 5.347 LHi. The actual discharge is smaller, being, 
according to the following authorities: 

One suppressed'. 


Both end contractions 
suppressed. 


Full contraction. 


Francis. . .g a = 3.33L// 2 


Smith. . . .<7a = 3.29 \L +y) 


3.33 (i-jo) Hi 
3.29 LH% 


3.33(L-0.2H)//2. 

3.29(i-~) h ! . 


(L should not be less than 3//.) . 

For flow over a sharp-crested weir without lateral contractions, air 
being freely admitted behind the falling sheet of water, 

Qa = [0.425 + 0.21 (^f^) 2 ]8.02Ltf^ 

where U, = height in feet from bottom of channel of approach to the crest 
of weir (Bazin). 

In triangular notches at any depth is constant and therefore C is 

regular and may be taken as 0.617. g 

q a = * z CLH^2g = l.S2LHl For a 90° notch, L = 2H and q =2.64 

for a 60° notch, L = 1.1557/ and g a = 1-524//-. 

q a XGXH (available height of fall) 
The Horse-Power of a Stream -- 555 

Fritftion in Pipes is independent of the pressure but is proportional 
to the wetted surface. iLioc Av 2 = fiAv 2 , at moderate velocities, and, as 

1.03G = 2f7, Fn =1.03/uGA|^. 

If a cylindrical body of water (length L, diam. D ) move at a velocity 

* _ _ ... , K DLj V 

v, through the pipe, Fn per sq. ft. of sectional area = 1.03/iG^ 2§xD 2 2 g 

Lj 

= 4.12ju^ XGX^r, and ,&sH = P-i-G, the Head Lost in Friction = 4.12^ • —• 
D y 


to* 

























hydraulics and hydraulic machinery. 109 

to 0 01 tor pipes> and 0009 

diam. in in. (Pelton Water'wheel^Co.*) _L(4?;2 + 5t, - 2 )-*-l>000rf, where d = 

A (hydraulic 

nation ofpSf ?£'„! c <f SSE 

ffi ^xllKKEESAHi&sg 

Flow of Water in Open Channels. (Kutter.) 

Slone 6 r-n a oIffi f W f t T SUI t ace in any distance-said distance = sine of 
and hadn? thp^nT . dependin g on , the character of the channel surface 

detritus, 0.05. eeds, 0.035, torrents encumbered with 

Tutton’s formula for pipes may also be used as herewith modified, where 
C has the values given for Rutter’s formula : v^—Ri Si. 

head due to velocity, ~ Floss due to friction. The friction loss varying 

U th “ & P -?^ d a.U b he^ 23 

duce* fric*Ion alResistances’ 1 ttf’flowRtiR yste ms W of SSjf •&«* P~- 

VV ater discharged into a basin delivers all of its energy as shock hut 

S^nVofS&^t 

J'Angies^and Elbows? Loss ® of" head?^Let' 0 ~n b ^f 
degrees of the angle through which the direction of flo^Ts deviated Then 
for/? 20 40 60 80 90 100 190 ia n' 

c= 0.046 0.139 0.364 0.74 0.985 1 26 1 861 2 431 


Loss of head - c • yfo • • c depends on the ratio of the radius 


Bends. 

180 Zg ---~ ‘" WVJ 

ot the pipe (0.5D) to the radius of curvature of the bend ( R ) 

0.5D-rR= 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 8 0 0 i no 

c= 0.131 0.138 0.158 0.206 0.294 0.44 0.661 0.977 1.408 1.978 
Gate-A’alves. Loss of head due to partial opening = c.r 2 -f- 2g. 


Opening = £ £ £ 

c= 98 17 5.52 

Cocks. Loss of head = ci> 2 -2//. 


£ 


£ 


2.06 0.81 0.26 0.07 


Opening = £ 
c = 222 


i £ 
52.6 21.1 


7.8 


£ 

2.8 


i 

0.92 


i 

0.2 








110 HYDRAULICS AND HYDRAULIC MACHINERY. 


WATER WHEELS. 

Pressure on Yanes. Force causing momentum =— /, and,as f = v-t, 
Pf = wv + a or> pressureXtime (i.e., impulse exerted) = momentum gener- 
ated If °t = 1 'sec. and w = weight of water passing per sec., wv ■ a <■ g 

° f F^TpiXl>r^ r flxed '(its' velocity being 0). + 

<<? Flat Plate sieving in the Direction of Jet. of plate = f ^el. of 

MfoiW 

^ Moving Hemispherical Surface or Cup. Relative velocity of jet and 
whPT, mpetin^=i),-v 2 (forward), and when leaving, -Vi v 2 (bacK^ 
ward). Consequently, the absolute discharge velocity -cup velocity 
relative backward velocity, v u whence, 

GA( vi-V 2 )v\ GA{v\ — ^GAXvi _ V 2 j_ ' Jf V2 = Vl -H2, the abso¬ 

lute velocity of rejectio? = 0, and all of the jet energy is exerted on the 

CU Wheel with Radial Vanes, a vane being constantly before the jet: 
Momentum before impact, =(GAvi)v after, (GAvi)v 2 • 0, 

GAvi(v\ — vo) 

Wheel with Many Curved Vanes : p ™^ej>tum_before impaet.- 
Sll'oT&t facial In thl» case ami that nf the hemispherical cup 

Diame^r 

Ko a vf<all Etficiencv with radial lloats or \ ane^, oU /o , cui \ eu 

K-(^xT'A.^ U, S“ »Tl^4‘"‘fe 

of float curve (Fig. 23): From the center of wheel drawhdd)havea 
and make AOB=lb°. Let the jet (of thickness C, — £Xneaci) naxe a 
slope of 1 in 10. From the middle of jet, D, draw DE so that OZ)L -3 . 
Takl DE = 0.5 to 0.7Xhead, and from E strike the arc DF , which is the 
curve for the Poncelet form of undershot wheel. 


















turbines. 


Ill 


ciency P 7t)”o „“‘ Sed f< f ,r fal1 ? hanging from 12 to 70 feet. Effi- 

the n v y eiodty°o 7 f°tt waSf TeTo'T Per -e. = one-half 
which water strikes wheel should ho 2°9iT i V co J 1 , se O u ently, point at 

®rdE» 

to T °h'cS* Kr* Msrttr FC -* being ~ 

Ihese cups are made double, with a center fin which spIitV the £t an i 


TURBINES. 

Turbines are water wheels in which the motion is caused by the reaction 

f oatfof a tlfe w r )^r e T| etVVee t n statlonary guide blades and the vanes or 
noats oj the wheel, the water flow may be axial or radial ("inward or 

flH l'S ) ,!l | 1 , reC10n ; and lf slloul(1 he so deviated that it enters the wheel 
floats as nearly at a tangent as possible, and leaves either radially or in a 
direction paraliel to the axis as the case may be. y ° r in a 

Radial Outward-Flow Turbines (Fourneyron type). Q = cu. ft. water 
passing per sec. under a head of H feet. Inner radius /?, =0 "iVfwAtT' 

«°=l5° r ?o30^ wVe o? e h e r^ 5 t0 1-5- . Ang e ie at°en?ran& 

a lo to 30 . Angle ot bucket at same point, /? = 2« + 20° to 30°. The 


velocity of wheel at Ri = v j = 


V 


2 all 


2 sin 0 cos 


(If a = 15°, 0 = 60°, C = 


sin (0- 
1.5, Vi = 4.8WW.) 


V“ + 0.lf ( ) 2 +c 2~[' 

*) (_ ^sin (/? — «)/ J 


Area of cross- 


v ***\«. J * t'l •’’HI }J m 

a bucket, I) — B-=\ = 2 to o, inversely 
-Thickness of metal floats, T = 0.015/?. 

IT sin a\ "1 

~2 - ) • Number of guides, N^ — XA -i-D 2 . No. 


3: sin 3 = 


Velocity at R = v-=-cv ] ; r.p.m. = 60v-r- 2xR = 9.55v + R. 

Velocity through guide passages, v 2 *=v l sin 0-hsin(a — 0) 
section of all openings = Q -r- v 2 = A = Q sin (a — B )-+-v, sin ft 
If D = depth and B = width of ' ’ ~ ~ 

according to the head of water. 

AT , + /fc«r 

2r.R\ sin a | \ 

of wheel buckets, A r = Ai sin 0 H-sin a. Angle of discharge 
(A 1 +NTD)-t2t:RD, where A, =area of discharge openings 

Curvature of floats (Fig 25): :Draw CAB = 9, drop CB perpendicular to 
AB. AL) Ahj B . 2. feet off BF and BQ^AD. From F strike tho 
arc HD - Draw DK-CL, making BDK = 180° —0, and join CK. Bisect 
CA at M and draw the perpendicular MN. Draw arc DL from N as a 
center. Draw PL anti CP, each inclined to CL by «°. From P as a 
center strike the arc RL of guide blade. Inward-flow turbines are designed 
similarly, but in an inverse manner. 

Axial or Parallel-Flow Turbines (Jonval type). The guide blades 
in this type are arranged in the form of a ring above the wheel vanes the 
water flowing parallel to the axis. These wheels work best when sub¬ 
merged in the tail-race or connected thereto by a draft-tube whereby the 


120 c 


-O-- - - -- - " ^ Vi vy » Cb UlOlflUUC VVI'cHJU 

suction of the latter may be availed of. a =15° to 25°, /? = 100° to 
Velocity, v, same as velocity r, of the Fourneyron wheel where c= 1 Veloc¬ 
ity of entering water=t;j =v sin 0-hsin(0~a). Total sectional area of en¬ 
trances between guides, A=Q + v j; total discharge area, A^Q-i-v. Mean 
radius, R = (R x +R 2 )-±2; radial width of operative ring of wheel I) = 
R 2 -Ri = 0AR, and #,=0.81?; Ro=1.2R. X = D-i-B — 2 to 4 

-/ A 


R, approx. 


T = 0.02R. No. of guides, JV 1 = (i-i-lfl))4. 


O.Sir sin a ’ 

(lA-hD 2 ); No. of floats, A r = Nj sin 0 -s- sin a. Sin 3 = (Aid- NTD) + 2-nRD 
R.n.m. = 9.55v-i-R. Height of wheels(0.5 to 0.6)1?. 

Curvature of floats (Fig. 26): Both the guides and floats are warped 
surfaces generated by a line at right angles to the axis, whose outer end 

















CQ 


112 HYDRAULICS AND HYDRAULIC MACHINERY. 


follows the curves in the figure. Draw AS inclined to the ,tlane of wheel 
by and similarly DC at 8°. Draw BF perp. to AB. b rom F as a cen 



F 

E 

\ / x* / 

\BX / 

-V 

- -^1=—vG- 

----/ *_/- 

A t\ 




C 


Fig. 26. 


Fig. 25. 

fpr strike the arc BE. Draw DG perp. to DC, make angles GDA = DAG = 

2 , and from intersection G, as a center, draw arc DA. The lowe 
carts of guide and float (AB and CD) are straight lines. 

Trnnul^p Turbines (Girard type) are parallel-flow wheels with 
wheel ^passages so enlarged toward the outlet and ventilated that they 
are never entirely filled with water, the energy being purely due to velocity. 
They are regulated by entirely closing a number of the guide Passage , 
the efficiency (GO to 80%) being therefore unimpaired by fractional open- 

Modern Practice. (From articles by J. W. Thurso in E. N., Dec., 02.) 
For heads less than 20 ft use radial-inflow reaction (Francis) turbines with 
vertical shafts -far heads of 20 to 300 ft., the same, but with horizontal 
shafts; for heads exceeding 300 ft., use radial, outward-flow, free-devia- 
tion turbines with horizontal shafts, or Pelton wheels. , . 

Parallel-flow turbines are now largely abandoned on account of their 
Door regulating qualities. Free deviation may be obtained 'with an e - 
ciency of 70% at 0.2 gate, and 80% at full gate; reaction turbines with 
60% efficiency at 0.2 gate and 78% at full gate. (Highest eff., 80% 

be ReSion ^“s^either regulated by making the guide-vanes mov- 
able so that the openings may be reduced according to load and without 
materially altering the direction of flow, or, the guide and wheel vanes aie 
divided by crowns into three or more superposed turbines any number 
of which may be shut off by a cylindrical gate according to load, allowing 
those Tn operation to work at full gate and at the correspondingly higher 

e-deviation turbines to attain high efficiencies must work in the free 
air and in order to obtain the advantages of draft-tubes, they must be 
supplied with air-valves which will automatically keep the water-level 

be Draft-Tubes > ' The^usfof draft-tubes permits turbines to be mounted 
on horizontal shafts and also to be set above the tail-water without -Oss 
of a oart of the head. The hanging water-column in the draft-tube is bal¬ 
anced by atmospheric pressure and could theoretically attain a height of 
31 ft. if the water were at rest,—but, with the water in motion, it ca 

exceed (34 — —) ft., where V = velocity of water in ft. per sec. When 

\ 2j/ 
























PUMPS. 


113 


leaving the draft-tube v should not be less than 2 ft per see. when starting 
at full capacity, not less than 3 ft. per sec. for variable loads over half 
capacity, and from 4 to 6 ft per sec. for widely fluctuating loads at times 
of small capacity. The a bsolute velocity of the water issuing from wheel 

in ft. per sec., Vx—c^2gH, where c = 0 285 for large turbines and low leads 
(10 ft.), 0.2 for medium turbines and heads (100 ft,.), and 0.167 for small 
turbines and high heads (500 ft ) II = total head in feet. 

When //= 10 ft., r>i = 7.23 ft per sec The head, h\ (due to velocity fli) = 
7.2Z 2 -±2g = 0.812 ft. Let v be the velocity at which water leaves the 
draft-tube = 3 ft.; the corresponding velocity head. /i = 3 2 = 2f7 = 0.14 ft.; 
the gain in head by using draft-tube =h l —h = 0. 812-0.14 = 0.672 ft., or 
6.72% of H. 75% of this gain should be realized in practice. 

Under average conditions, the greatest draft head, H permissible for 
vaiious diameters D of draft-tubes is as follows Z)=0.5 ft., H = 32.5 ft.; 
£> = 8 ft., II = 14.5 ft.; £> = 9 ft., H = 13 ft. £> = 13 ft.. //= 10 ft. From 

these heads should be deducted h(^ = ^r) due to velocity, v, of water leav¬ 
ing tube. Short draft-tubes of small diam. should extend from 6 to 12 in. 
below surface of tail-water,—long tubes of large diam. from 20 to 24 in. 
below. Tubes should have a gradual taper, enlarging towards the tail- 
water, in order to reduce the velocity of the discharge and to thus avoid 
shock 

The H. P. of a Water Wheel =GqHr) = 550, where ^efficiency of 
wheel. As the water has no forward momentum on leaving the turbine 
(or on entering a centrifugal pump), each lb. undergoes a change of momen- 
tum=v-f-g, where v is the forward component of the entering velocity 
(leaving vel. for centrifugal pump). Let v\ = velocity of wheel-rim; then, 
useful w T ork per lb. water = (vvi-i-g) ft.-lbs. per sec. =i ?/£. 

High-Efficiency Turbines. Samson (Leffel) and McCormick (S. 
Morgan Smith & Co.) turbines tested at the Holyoke flume under heads 
of about 15 ft. show efficiencies of over 80% at full and f gate, and a 
maximum of about 85% at $ gate. 

Losses in Turbines. Surface friction and eddying, 10 to 14%; energy 
rejected into tail-race, 3 to 7%; shaft friction, 2 to 3%. 


PUMPS. 

Centrifugal Pumps are simply reversed turbines in which the applica¬ 
tion of mechanical pow r er to the wheel transforms velocity into pressure 
and elevates water to the same height (neglecting losses) as the head 
would be for a turbine running at the same speed. The radial outward- 
flow type is best adapted for pumping. Water may be raised through 
suction up to 26 ft., and, using as a force-pump, may be elevated upwards 
of 100 ft. by well-designed wheels. 

It is claimed for the Worthington volute type that it will work up to 
heads of 85 ft., and that tests have shown an efficiency of 86%. 

A Swiss pump (Sulzer Bros., wheel diam. of 20 in., 890 r.p.m.) tested 
in 1902, lifted 1,010 gal. (135 cu. ft.) per min. against a head of 428 ft., 
or, as pump was four-stage, 107 ft. head per wheel. Efficiency, 76%. 

A single-stage De Laval pump (runner diam. of 13.75 in., 1,545 r.p.m.) 
driven by a 55-H.P. steam turbine of same make (tested by Profs. Denton 
and Kent in Apr. ’04) lifted 1,760 gal. per min. 100 ft. with an efficiency 
of 75%. Duty, condensing, 61,860,000 ft.-lbs. per 1,000 lbs. of com¬ 
mercially dry steam (moisture <1.7%) and 45,000,000 ft.-lbs. per 1,000 
lbs. steam (non-condensing). . ntn 

A two-stage pump of same make (runners 9 in. and 2.84 in. diam., 2,050 
and 20,500 r.p.m. respectively) lifted 244 gal. per min. 781 ft. Duty, 
48,880,000 ft.-lbs. per 1,000 lbs. steam. Steam per water-H.P. (lbs. water 
lifted per sec. X lift in ft. -s- 550) = 40.5 lbs. per hour. 

Proportions. Let R = wheel radius, and R\ — — = radius of water inlet. 

Diam. of disch arge-pipe, D = 0.36 Vq -j- V 2gH. Diam. of wheel = 2P 

-O.IsVqTVW. To draw curve of wheel-vane: .Let r, == velocity of 
inflowing water. Draw radius R\ at distance R\ on this radius draw a 







114 HYDRAULICS AND HYDRAULIC MACHINERY. 


line inclined outward to li by angle «, whose tangent = 0.01 ^ o 

(N = r.p.m. Q = cu. ft. per min. t>j = ft. per sec.). 

The vane curve must be tangential to this line. At the extremity of a 

. ,/ R*-R x \ 

radius draw a tangent and on this tangent, at a point distant L l s iTT7t/ 

as a center, strike an arc from the outer circumference of wheel to the 
inlet circumference, and this arc will be the vane curve. 

The case should start at zero cross-section and increase in one circum¬ 
ference to full discharge section by means of an Archimedean spiral. 

Hydraulic Ram. Water flowing in a pipe under a low head escapes 
through an opening at the end until it acquires a velocity sufficient to move 
a valve closing the outlet. This sudden stopping of flow creates an ex¬ 
cessive pressure in the pipe, and a valve near the end is opened which 
leads to an air-chamber into which the water rushes, and from there into 
a delivery-pipe. Equilibrium being restored the air-chamber valve closes, 
outlet valve opens and the cycle is repeated. Water may be raised 10 
times as high as the head of the stream in ft. Efficiency, 50 to 75%. 

Pulsometer. In this device water is raised by suction into the pump 
chamber by a vacuum resulting from, the condensation of steam within 
it; it is then forced into the delivery pipe by the pressure of a fresh supply 
of steam. Two chambers are employed, one raising while the other dis¬ 
charges. Duty, 10,000,000 to 20,000,000 ft.-lbs. per 1,000 lbs. of steam. 

The Air-Lift Pump. A vertical pipe with its lower end submerged 
in a well or tank is supplied with a smaller pipe from which compressed 
air enters into the bottom of the larger pipe. 

The column of liquid in the pipe, consisting to a certain extent of air- 
bubbles, is lighter than an equally high column of liquid not so aerated, 
and therefore rises. The efficiency ranges from 25 to 50%, where the 
ratio of submerged length to length above surface varies from 0.5 to 2, 
respectively. As there are no moving parts, this device is valuable in 
the case of lifting acids, chemical solutions, sewage, etc. 


PLUNGER PUMPS AND PUMPING ENGINES. 

Quantity of Water Pumped. Q (in cu. ft. per min.) =0.00545 Vd 2 \ 
Qx (gals, per min.) = 0.040766 Vd 2 , where V = speed of plunger in ft. per min. 
and d = diam. of plunger in in. V ranges from 100 to 200 ft. per min., 
anil in well-designed engines may reach 250 ft. if the waterways are ample 
and the water is not abruptly deflected. Loss by leakage and slip 
ranges from 5% for new, well-packed pumps to 40% for worn and badly 
cared-for apparatus 

H. P„ Required to Raise Water a Given Height, H. (Theoretical.) 

H.P. = QH h-529.2 = Q\H -f-3,958.7, or, as 1 ft. // = 273Mb. pressure, p, 
H.P. — Qp-^- 229.2 = Q\P 1,714.5. Theoretical lift for normal temperatures 
= 34 ft. When the temperature of the water increases, the pressure of the 
water vapor decreases the theoretical lift, which at 15Q° F. = 25.7 ft., at 
175° F. = 18.5 ft., and at 200° F. = 7.2 ft. Hot water should therefore 
flow to the pump by gravity. 

Air-Chambers. Even flow and smooth running are obtained by the 
use of air-chambers, where the impact of the water is received and given 
out as pressure. On the delivery side these should be from 3 to 6 times 
the capacity of pump, and on the suction side from 2 to 3 times the capacity. 

High-Duty Pumping Engines. Small pumps are either driven from 
a crank-shaft or are direct-acting, i.e., having a steam cylinder in which 
the full pressure of the steam is used throughout the stroke. In large, 
high-duty engines the steam is used expansively. 

In the Worthington high-duty engines compensating cylinders are em¬ 
ployed in order to equalize the driving force. These cylinders rock on trun¬ 
nions, are connected to an accumulator under a water pressure of about 
200 lbs. per sq. in., and have their plungers pivoted to the pump-rod. 
This arrangement offers a resistance to the steam pressure during the 
early part of the stroke, receiving energy during the period of full steam 
p-essure and giving it out later when the pressure falls through expansion, 
thus maintaining a fairly even effective pressure throughout the stroke 

Duty. The old measure of numning-engine performance was the number 
of ft.-lbs. of work done per 100 lbs. of coal consumed. In 1891 the A. S. M. E 



PLUNGER FUMP.S AND PUMPING ENGINES 


115 


committee recommended that it be changed to the number of ft.-lbs. of 
work per million heat units furnished to the boiler ( = 100 lbs. coal where 
each lb. imparts 10,000 heat units, or where the evaporation from and 
at 212° F. = 10.355 lbs. water per lb. of fuel). It is customary now to 
also state the duty in terms of the number of ft.-lbs. of work per 1,000 lbs. 
of steam used. 

Performance of a Modern Pumping Plant. The following data are 
taken from a 24-hour duty trial of one of the units of the Central Park Ave. 
pumping plant in Chicago (E. N., 5-26-04), and will serve as an illustra 
tion of high-grade installations. 

Three Worthington high-duty, triple-expansion engines make up the 
plant, each with a rated capacity of 20,000,000 gals, per 24 hours against 
150 ft. head. Cylinders are 21, 33, and 60 in. in diam., 50 in. stroke, 
steam-jacketed all over. Superheated steam is used which is supplied 
by six 225 H.P. Scotch marine boilers, each with two 40 in. corrugated 
Morison furnaces and 140 24 in. tubes. Boilers are 10 ft. in diam. and 
12 ft. long, fitted with Hawley down-draft furnaces. 

Steam pressure at throttle, h.p. and i.p. jackets and reheater coils, 
114.45 lbs.; at l.p. jacket, 10.13 lbs. Vacuum in exhaust, near l.p. cyl. = 
26.98 in. of mercury, barometer, 14.45 lbs. (The weights of pistons, plungers, 
etc., are exactly balanced by a water pressure of 78.97 lbs.) Delivery 
pressure of water = 52.23 lbs. = 120.65 ft. head. Height of delivery 
gauge above water = 32.24 ft. .’. Total head = 152.89 ft. Temp, of 
water = 72° F., temp, of feed-water = 102.18° F., temp, of steam at throttle = 
516.91° F. (superheated 154°) Total steam used in cylinders = 143,734 
lbs. Steam used in jackets and reheater, 16,400 lbs. Total steam used, 
160,134 lbs. Dry coal burnt to evaporate total steam, 18,534 lbs. R.p.m., 
19.33. Piston speed, 159.74 ft. per min. Stroke, 49.587 in. Plunger 
displacement (24 hrs.), 22,086,318 gals. = 2,952,400 cu. ft, = 183,934,538 lbs. 
Allowance for leakage and slip, 0.5%. Net work (24 hrs.), 27,981,142,800 
ft.-lbs. Net delivered H.P =588.82. I.H.P. = 660.9. Efficiency. 89.15%. 
Steam per I.H.P per hr., 10.01 lb.; do., per net delivered H.P , 11.32 lb. 
Dry coal per I.H.P. per hr., 1.42 lb.; do., per net delivered H.P., 1.58 1b. 
Combustible per I.H.P. per hr., 1.07 lb.; do., per net delivered H.P., 1.2 lb. 
Duty per 1,000 lbs. steam = 174,735,801 ft.-lbs. Duty per 100 lbs. coal = 
150,971,958 ft.-lbs. 4 . __ 

Boilers Fuel, Maryland Smokeless coal. Upper grate surface, 35 sq. ft. 
Water heating surface, 1,402 sq. ft. Superheating surface: internal, 
180 sq. ft., external, 375 sq. ft. Total coal burnt, 22,779 lbs. Per cent 
moisture, 0.88. Total dry coal, 22,519 lbs. Per cent ash and refuse, 
8.17. Total water fed to boiler, 195,153 lbs. Factor of evaporation 
(including superheat), 1.166. Equivalent water evaporated into super¬ 
heated steam from and at 212°, 227,548 lbs. Dry coal per hour per sq ft. 
of upper grate surface, 26.87 lbs. Equivalent evaporation from and at 
212° per sq. ft. of heating surface, 6.7 lbs. Average steam pressure, 
154.22 lbs. Temp, of feed-water entering purifier, 177.26 4. lemp. 
of escaping gases, 459° F. Degrees of superheat, 162 H.P. developed, 
275. Actual water evaporated per lb. of coal fired, 8.o67 lbs. Equivalent 
evaporation from and at 212° F.: of coal fired, 10.077 lbs.; of dry coal, 
10 11 lbs.; of combustible, 10.97 lbs. Calorific value of dry coal per lb., 
14 213 B T U • do of combustible, 15,634 B.T.U. Efficiency of boiler 
(based on combustible), 67.76%; do., including grate (based on dry coal), 
64 52%. Cost of coal per ton of 2,000 lbs., $2.89. Cost of coal to evaporate 
1,000 lbs. water from and at 212° F„ $0,151. A similar engine at 142 27 
lbs. steam pressure, 71.2° superheat gave a duty of 157,133,000 It.-lbs. 

Pe The°h?ghest re e coTded e duty (181,068,605 ft.-lbs. per 1 000 lbs. dry steam) 
is that of an Allis triple-expansion pumping engine at St. Louis, operating 
under 140 lbs. steam pressure. Another high-duty engine is a Reynolds 
triple-expansion vertical engine at Boston, 30,000,000 gals, capacity, 
SSaPiston speed of 195 f^per min under 185 lbs steam pressure 
Duty, 178,497,000 ft.-lbs. per 1,000 lbs. steam, or, 163.92o,300 ft • -lbs • 
per million heat units. B.T.U. per I ITP. per mm.196. Steam per 
I.H.P. hour = 10.375 lbs. Coal per I.H.P. hour-1.06 lbs. Ihermal 
efficiency, 21.63%, or, including economizer, 22.58/ 0 . 




116 HYDRAULICS AND HYDRAULIC MACHINERY. 


HYDRAULIC POWER TRANSMISSION. 

Water under high pressures (GOO to 2,000 lbs. per sq. in.) is advantageously 
used where power distribution is desired over small areas, viz., wharves, 
boiler and bridge shops, for presses, cranes, riveting, flanging arid forging 
machinery. Tne system consists of pumps to develop the desired pres¬ 
sure, from which the water flows through piping to an accumulator, which 
is a vertical cylinder provided with a heavily weighted plunger. Pipes 
lead from the accumulator to the machines .to be operated. The work 
stored in an accumulator is equal to the weight on plunger X height in ft. 
plunger is raised, or wH ft.-lbs. Accumulator efficiency may be 98%. 
Efficiency of a direct plunger or ram in a hydraulic crane is around 93%, 
decreasing in proportion to the number of multiplications of movement 
by pulleys. (Pressures used in boiler shops range from 1,500 to 1,700 lbs. 
per sq. in.) Effective pressure (lbs. per sq. in.) = accumulator pressure 
(lbs. per sq. in.) X (0.84 — 0.02 m ), where w = ratio of multiplying power 
(H. Adams). 

Maximum hoisting speeds in ft. per sec., warehouse cranes, 6; plat¬ 
form cranes, 4; passenger and wagon hoists, heavy loads, 2; plunger 
passenger elevators, direct stroke, 10. 

Cast iron should not. be used for hydraulic cylinders when pressures 
over 2,000 lbs. per sq. in. are used, W. I. or steel being substituted. The 
test pressure should be about three times the working pressure. 

Design of Hydraulic Cylinders. (Kleinhans.) Load on ram, in 
tons = 0.0003927pd 2 ; thickness of walls of cylinder in in. = pD-r-2(f-~ p); 

thickness of bottom end of cylinder - at center = 0.5 D^p-i-f] thickness 

(at a radius D-h 3) between center and wall diam. =0 A33D^p -5-/; where 
p = water pressure in lbs. per sq. in., d = diam. of ram'or plunger, Z) = internal 
diam. of cylinder = d+l to 2 in., according to size, / = safe fiber stress = 
10,000 for cast steel. The bottom of cylinder is spherical (of radius d ) and 
rounded, to wall of cylinder by a radius = 0. 2d. 

Friction of Cup Leathers. F = frictional resistance of a leather 
in lbs. per sq. in. of water pressure =0.08p + (c-t-d), where d = diam. of 
plunger in in., p = water pressure in lbs. per sq. in., and c = 100 for leathers 
in good condition, 250 if in bad condition. (Goodman.) 





i 


SHOP DATA. 


THE FOUNDRY. 

Sand. Good, new sand contains from 93 to 95% of silica nf oi„ 

az & of fsr„d and oiri d n e d 

&T/wethtT d ' ^ a ~' ! ^ 

chaff a horse °G cla £-’ r ,9 ck sand - powdered charcoal, cow hair 

in a mill manure ’ etc - (for binding power and porosity) ground together 

Cores require a mixture of rock sand and sea sand with a binding sub 

ch^rco'a ^and^l^j^ wa^en aS ^* e ^ ^ b&king with a StSSCIS 

frr^ artil ?^ Sand * Powdered blast-furnace slag, brick dust or fine dust 
from castings may be used for this purpose. P urnbago nowdcred nhsr 
coa , soapstone, and French chalk ire used for Scfng’mouddf fn order 
that, smooth castings may be obtained. S mourns in order 

A'OOSisteney of Sand. If too much burnt, or old sand is used it will 
on k a Zifr??' 11 * Sa , n< . 1 , should be so moistened that if the hand is closed 
given to it f a ° d the " opened> the sand wil1 just retain the shape 

under^^^shof.ld^ 81111 ^!* f a ? terns having one horizontal dimension 
a ? er ^ in - should be made in. smaller to allow for rapping Under 

mall c 9 ndltl pns the shrinkage of castings per foot is as follows^’ cast and 

malleable iron, i in.; brass, aluminum, and steel, * in.; zinc, & in ; Un 
& •’ ^hite metal, & in., gun-metal, £ in. The edges of patterns should 

be rounded, all corners and angles being filleted in order to avoid the 
weakening due to crystallization in cooling. Kl the 

H eights of Castings. Multiply weight of pattern by 12.5, 14.1 or 
16.7, respectively, if the pattern is of red, yellow, or white pine and the 

by 14 . 2 .‘ S 16 ? ol r ia CaS ‘ ing iS ° f ye! '° W brass ' “ultiSly sfmilarly 

a r® c’‘e an and Brighten Brass Castings. In a glazed vessel mix 
3 parts of sulphuric acid with 2 parts of nitric acid and add a handful 
taWe sak to each quart of the mixture. Dip the castings in the mixture 
and then thoroughly rinse in water. 1 e 

The Cupola. Speed of melting: W=2d 2 ^ / p. Air required - Q = 0.5d 2 ^p. 

H. P. to operate fan = p+ 3,800. In these formulas d = inside diam. 
of cupola lining in in., IF = lbs. of iron per hour, p = air pressure at cupola 
in ounces per sq. in., and Q = cn. ft. of air per min. (E. N., 7-21-'04). 

THE BLACKSMITH SHOP. 

i Wrought iron welds at a white, sparking heat (1,500° to 

I, GJ0 b.), sand being used as a flux and to prevent scale. Steel welds 
at lower heats, borax being the flux employed. 

Electric \\ elding. Extra sound welds can be made by abutting the 
surfaces of the parts to be welded, allowing an electric current of large 
volume to now, and by forcing the parts together when the localized 
heat at the joint (due to the current) has attained the welding tempera¬ 
ture. Ab^™ atin g currents of low potential are used. In general, from 
Zb to 60 II.P. applied to the generator are required per sq. in. of section 
to be welded. For iron and steel this power must be applied for [(area in 

117 





118 


SHOP DATA. 


so in x 18)4-10] seconds Copper requires 82 H.P. per sq. in. of section, 
and it must he applied [(area in sq. in.X 17.5)4-7] seconds. . 

To Anneal Tool Steel, heat to an even red and cool slowly in a box, 

su rounding the steel by gravel and charcoal. , , , 

Case-IIardening, Raise the pieces (W. I. or mild steel) to a red heat, 
and apply equal parts of prussiate of potash and salt. Quench while the 
mixture is flowing, not waiting until it burns off. If. extreme hardness 
desired use cyanide of potassium. (A dangerous poison.) 

Tempering of Steel. Harden by heating to a dark red (about 1,300° F.), 
oooline quickly in water, the article being kept in motion. To temper, 
brightenthe surface of the article and heat slowly (not in contact with 
the flame) until the desired color (as below) appears, and then quench 

in Very Va^ 0 straw (430° F.), for brass scrapers, hammer faces, lathe and 

planer tools for steel and ivory, and bone-working tools 

Light straw (450° F.), for drills, milling cutters, lathe and planer tools 
for iron. „ . „ 

Medium straw (470° F.), for boring cutters. x . 

Very dark straw (490° F.), for taps, dies, leather-cutting tools. 
Brown-yellow (500° F.), for reamers, punches and dies, gouges, stone- 

° U Yelk)w°purple (520° F.), for flat drills for brass, twist drills, planes, 
light purple (530° F.), for augers, dental and surgical instruments. 

Dark purple (550° F.), for cold-chisels, axes. . 

Dark blue (570° F.), for springs, screw-drivers, circular saws for metal, 
wood-chisels, wood-saws, planer knives and moulding cutters. 

Forgings. Allowance for Machining. 

'.up to 5 in. 6 to 8 in. 9 to 10 in. 12 in. and larger 

Allowance. 0.25 in. 0.375 in. 0. 5 in. 1 in. 

THE MACHINE SHOP. 

Punches and Dies. Diam. of hole in die = diam. of punch 4-(0.16 to 0.3) 
X thickness of plate to be punched, according to various authorities A 

fair average value for the excess is 0.2 X thickness. . 

Cutting Speeds for Lathes, Planers, and Shapers in ft. per mm. 

(Ordinary tool steel.) 


American 

Practice. 


German. 
(Ing. Taschen- 


(J. Rose.) 

buch.) 

6 to 10 

12 

12 

15 to 20 

18 to 30 

18 ‘ 

‘ 35 

18 “ 30 

20 ‘ 

‘ 38 

16 “ 24 

60 ‘ 

‘ 120 

40 “ 90 

150 ‘ 

‘ 350 

40 “ 9p 


Hard cast steel. 

Tool steel. 

Machinery steel. 

Wrought iron. . .. 

Cast iron. „. 

Bronze. 

Copper. 

Pi mi referential speed, ft. per min. = 0.2618 X r.p.m. X diam. of piece in m. 
Planer speeds rangetrom 18 to 22 ft. per min. Maximum Feeds and Depth 
Cuts (Ing Taschenbuch): max. feed per rev. = 0.06 in. for roughing, 
and 1) 2 in. for finishing; greatest depth of cut = 0.4 in. for C. I., =0.28 in 
r yr j = o K 3 in for steel, =0.12 in. for bronze. Max. planer feed 
per stroke = 0.08 to o’.lG in. for roughing, and 0 12 to 0.5 in. for finishing; 
greatest depth of planer cut = 0.8 in. for C. I., =0.5 in. for W. I., = 0.32 in. 
fn- vfeel =0.16 in. for bronze- 

Milling Cutters. (Ordinary tool-steel.) Angle of tooth: Front 
fare radial; tooth angle, 50°; angle at cutting edge = 85 (5% clearance) t 

No of teeth = 2.8 (diam. in in. 4* 2.6 in.). Take nearest even number. 


Speed, Depth Feed, 

ft. per of cut, in. per 
min. in. min. 

Hard steel. 21 rz i 

Wrought iron. 40 1 

Mild steel. 30 

Gun-metal. b0 t t 

Cast-iron gears. 36 * ? 

Hard cast iron. 30 3$- ts 

















119 


MACHINE SCREWS. 


F°r fight cuts, speed in ft. per min.: steel, 45; W. I., GO;C. L, 90; gun- 
met al ,_ 10,); brass, 120. lor heavy cuts reduce these speeds about one-half, 
rwlst Drills (of ordinary tool-steel). Revs, per min for iron: 4 in 

K\ n -’J 20 '’a& o 11 -’ 2 ?£ : t. in - 160; f in., 130; f in., 105; 1 in., 80; 
1 £ in., 54, 2 in., 39, 3 in., ~ 6 ; 4 in., 17„ For steel take 0.7 of these speeds.— 
for brass, multiply them by 1.25. 

, Feed: 125 revs, per inch depth of hole for drills under 4 in.; for larger 
drills allow 1 in. of feed per min. 


Morse Standard Tapers for Drill Shanks and Sockets. 




Diam. 


C. to c. 
of slot 
drill- 
, hole. 




No. of 
taper. 

Large 
diam. of 
socket. 

ft in. 
from bot¬ 
tom of 
hole. 

Depth 
of hole. 

Width 
of slot. 

Diam. 

of 

tongue. 

Length 

of 

tongue. 

1 

0.475 

0.369 

2ft 

* 

0.213 

0.33 

-ft 

2 

0.7 

0.572 

2* 

i 

0.26 

hi 

1 

3 

0.938 

0.778 

31 

l 

0.322 

i 

ft 

i 

4 

1.231 

1.026 

4i 

1 5 

1 6 

0.478 

3 1 

rnf 

5 

1.748 

1.475 

5i 

li 

0.635 

1M 

4 

6 

2.494 

2.116 

7# 

U 

0.76 

2 

i 


The tongues of drills are 0.01 in. less in thickness than the -width of 
slot. Keys to force out drills are tapered i.75 in 12 (or 8° 19'). 

Taper Turning. Distance tail-center is to be set over = 

tota l length of piec e v , diff. between diam s. at ends of taper 
length of tapered part 2 

As the centers enter the work an indefinite distance, this rule is only ap¬ 
proximate and the results must be corrected by trial. 


Machine Screws. 


Wire 

Threads 

Diam. 

T*P 

Wire 

Threads 

Diam. 

Tap 

gauge. 

per in. 

in in. 

drill. 

gauge. 

per in. 

in in. 

drill. 

2 

56 

0.0842 

No. 49 

12 

24 

0.2158 

No. 17 

3 

48 

. 0973 

45 

14 

20 

.2421 

13 

4 

36 

.1105 

42 

16 

18 

.2684 

6 

5 

36 

. 1236 

38 

18 

18 

.2947 

1 

6 

32 

.1368 

35 

20 

16 

.3210 

i in. 

7 

32 

.1500 

30 

22 

16 

. 3474 

ft “ 

8 

32 

.1631 

29 

24 

16 

. 3737 

a •• 

9 

30 

.1763 

27 

26 

16 

. 4000 

xr • • 

6 4 

10 

24 

.1894 

25 

28 

14 

.4263 

‘ ‘ 

3 3 





30 

14 

.4520 

2J. * 4 

64 


Maximum lengths: No. 2, 4 in.; No. 4, f in.; No. 6, 1 in.; No. 8, 1} in.; 
No. 10. H in-i No. 14, 2 in.; No. 18, 24 in.; No. 22 and larger, 3 in. 
Lengths increase by lGths up to i in., by 8ths from 4 to 14 in., and by 4ths 
above li in. 

International Standard Threads (Metric). Angle of lhread = 60°; 
flat i ht. of sharp V thread; root filled in ft lit. Dimensions in mm. 


Diam. 

Pitch. 

Diam. 

Pitch 

Diam. 

Pitch. 

6 & 7 

1 

18.20 & 22 

2.5 

48 <fe 52 

5 

8 & 9 

1.25 

24 & 27 

3 

56 & 60 

5.5 

10& 11 

1.5 

30 & 33 

3.5 

64 & 68 

6 

12 

1.75 

36 & 39 

4 

72 & 76 

6.5 

14 & 16 

2 

42 A 45 

4.5 

80 

7 


Metric threads may be cut in lathes whose lead-screws are jn inch pitch 
by introducing change gears of 50 and 127 teeth. (127 cm.=50 in., within 
0.0001 in. For less accurate work a 63-tooth wheel will give an error of 
only 0.001 in. in 10 inches.) 








120 


SHOP DATA 


Screw Threads. 


i 

TS 

I 

T6 

i 

A 

I 

i 

l 

1 

H 

n 

n 

n 

n 

n 

n 

2 

2i 

2| 

2f 

3 

3i 

3£ 

3i 

4 

4* 

4 

4i 

5 

5i 

5* 

5i 

6 


U. S. Standard. 


Diam. 
in in., 
d. 


Threads 
per in., 
n. 


20 

18 

16 

14 

13 

12 

11 

10 

9 


8 

7 

7 

6 

6 

5* 

5 

5 

4* 

4* 

4 

4 

3* 

3* 

3* 

3 

3 

2i 
2| 
2f 
2 * 
24 
2| 
2f 
2* 


Tap drills. 


U. S. 


T6 


72 

H 

1 3 
32 
7 

16 

* 

f 


If 

1_5 
1 6 

Ire 

i& 

i^r 

H 

H 

11 

iM 


‘V. 


64 

72 

ft 

ft 


6 4 
13 
16 

ft 

Itj 

li 

ltf 

I u? 

i U 

i :t 2 

I I r 
■* .12 
12 1 
i 52 


l-Si^aS 

)—( - 4 _i -+J X 


"O _■ 

<s c 

a> 3 +3 w 

J3 2 1 i | 

^{£.3 II O 

"O loQ TJ-O 
n ii c 3 


c /3 0 ) 

•- o 

C3 


Nuts—rough. 


co^ a-3 . 

- o . a 


cj O MJ-i 

X'C- 0 cx 


G II ' ■ g CO 55 fe' 
rr, "P . . 03 ^ * • 


. S o3 ‘ 

r-H ^ <D 


t>|laj|T's 5 i 3 

£■§* -i-So^SS 


Hex.— 
short 
diam. 


^’S-s 


W) 

atj 

CO 


Q.S S 


" CAJ 

^"5 Qi 1 
cj 03 O'rf 

£ 

•5:5 II 


I 

a 

i 

1 

k 

Its 

li 

lrg- 

If 

1H 

2 

2jt 

2 | 

2-4 

2 | 

2fi 

3| 

Si- 

Si 

4i 

4f 

5 

5| 

5| 

6| 

64 

6i 

7i 

71 

8 

81 

8| 

94 


Square— 
long 
diam. 


Whitworth. 


Threads 
per in., 
n. 


Diam. 
at thd. 
bottom. 


0.186 

.241 

.295 

.346 

.393 

.456 

.508 

.622 

.733 

.840 

.942 

1.067 

1.161 

1.286 

1.369 

1.494 

1.590 

1.715 

1.930 

2.180 

2.384 

2.634 


tC I 02 I C 1 I * 

-s a -g 5 03 -d 

H 2 2 « j3~_c 

c a °;sp >■ 

*3 - * > . 

r* 00 • bo 

p 2 c 

P"C M 2 . o'-r 
' U CD 03 c3 c .s^ 

X » 2' 

^ GO 0 ) C «« P P 

'X C ^ c3 l £ 

a»--< • - c 

- c U4<+-<~3 t-' 

O Js ^ O 

« 

• ^ rr h . . 

J3 • c O 03 5P 03 

t_.^S SjQ 0TJ 3 3 

^ || . -. »3 S 0^3 

li 03-—' C ^^3 


Stubs’ Steel Wire Gauge (continued from table on page 121). 


No. 

Diam. 

No. 

Diam. 

No. 

41 

0.095 

52 

0.063 

72 

42 

.092 

54 

.055 

74 

43 

.088 

56 

.045 

76 

44 

.085 

58 

.041 

78 

45 

.081 

60 

.039 

80 

46 

.079 

62 

.037 

A 

47 

.077 

64 

.035 

B 

48 

.075 

66 

.032 

C 

49 

.072 

68 

.03 

D 

50 

.069 

70 

.027 

E 


Diam. 

No. 

Diam. 

No. 

Diam. 

0.024 

F 

0.257 

P 

0.323 

.022 

G 

.261 

Q 

.332 

.018 

H 

.266 

R 

.339 

.015 

I 

.272 

S 

.348 

.013 

J 

.277 

T 

.358 

.234 

K 

.281 

U 

,368 

.238 

L 

.290 

V 

.377 

.242 

M 

.295 

w 

.386 

.246 

N 

.302 

X 

.397 

.25 

O 

.316 

Y 

.404 




Z 

.413 




















































WIRE AND SHEET-METAL GAUGES. 


121 


The U.S. Standard and Imperial gauges are respectively the legal stand¬ 
ards in the l . S. and Great Britain. Stubs’ steel wire gauge is used in 
measuring steel wire and drill rods. 


Wire and Sheet-Metal Gauges. 


No. 

Ameri¬ 

can, 

B. & S. 

Birming¬ 
ham— 
Stubs 
(iron). 

Stubs 

(steel). 

Wash¬ 
burn & 
Moen— 
Roebling 

Trenton 
Iron Co. 

U. S. 
Stand¬ 
ard. 

Impe¬ 

rial. 

0000000 




0.49 


0.5 

0 5 

000000 




.46 


.469 

.464 

00000 




.43 

.45 

.438 

.432 

0000 

0.460000 

0.454 

. 

.393 

.40 

.406 

.4 

000 

.409640 

.425 


.362 

.36 

.375 

.372 

00 

.364800 

.38 


.331 

.33 

.344 

.348 

0 

.324950 

.34 


.307 

.305 

.313 

.324 

1 

.289300 

.3 

0.227 

.283 

.285 

.281 

.3 

2 

.257630 

.284 

.219 

.263 

.265 

.266 

.276 

3 

.229420 

.259 

.212 

.244 

.245 

.25 

.252 

4 

.204310 

.238 

.207 

.225 

.225 

.234 

.232 

5 

.181940 

.22 

.204 

.207 , 

.205 

.219 

.212 

6 

.162020 

.203 

.201 

. 192 

.190 

.203 

. 192 

7 

.144280 

.18 

.199 

.177 

.175 

. 188 

. 176 

8 

.128490 

.165 

.197 

.162 

.160 

. 172 

.16 

9 

.114430 

. 148 

.194 

. 148 

.145 

.156 

.144 

10 

.101890 

.134 

. 191 

. 135 

. 130 

. 141 

.128 

11 

.090742 

.12 

.188 

.12 

.1175 

. 125 

.116 

12 

.080808 

. 109 

. 185 

.105 

.105 

.109 

.104 

13 

.071961 

.095 

.182 

.092 

.0925 

.094 

.092 

14 

.064084 

.083 

.180 

.08 

.08 

.078 

.08 

15 

.057068 

.072 

. 178 

.072 

.07 

.07 

.072 

16 

.050820 

.065 

.175 

.063 

.061 

.0625 

.064 

17 

.045257 

.058 

*. 172 

.054 

.0525 

.0563 

.056 

18 

.040303 

.049 

. 168 

.047 

.045 

.05 

.048 

19 

.035390 

.042 

.164 

.041 

.039 

.0438 

.04 

20 

.031961 

.035 

.161 

.035 

.034 

.0375 

.036 

21 

.028462 

.032 

.157 

.032 

.03 

.0344 

.032 

22 

.025347 

.028 

.155 

.028 

.027 

.0313 

.028 

23 

.022571 

.025 

.153 

.025 

.024 

.0281 

.024 

24 

.020100 

.022 

.151 

.023 

.0215 

.025 

.022 

25 

.017900 

.020 

.148 

.02 

.019 

.0219 

.02 

26 

.015940 

.018 

.146 

.018 

.018 

.0188 

.018 

27 

.014195 

.016 

.143 

.017 

.017 

.0172 

.016 

28 

.012641 

.014 

.139 

.016 

.016 

.0156 

.014 

29 

.011257 

.013 

.134 

.015 

.015 

.0141 

.013 

30 

.010025 

.012 

.127 

.014 

.014 

.0125 

.012 

31 

.008928 

.010 

.120 

.0135 

.013 

.0109 

.011 

32 

.007950 

.009 

.115 

.013 

.012 

.0101 

.0108 

33 

.007080 

.008 

.112 

.011 

.011 

.0094 

.01 

34 

.006304 

.007 

.110 

.010 

.01 

.0086 

.009 

35 

.005614 

.005 

.108 

.0095 

.009 

. 0078 

.008 

36 

.005000 

.004 

.106 

.009 


.007 

.007 

37 

.004453 


. 103 

.0085 


.0066 

.0068 

38 

.003965 


.101 

.008 


. 0063 

.006 

39 

.003531 


.099 

. 0075 



.005 

40 

.003145 


.097 

.007 



.0048 


Imperial Wire Gauge (continued from table). 

No. 41 42 43 44 45 46 47 48 49 50 

Diam.0044 .004 .0036 .0032 .0028 .0024 .002 .0016 .0012 .001 

Grinding Wheels. The abrasives used in grinding wheels are corundum, 
emery (impure corundum), carborundum and alundum. The first two 





























122 


SHOP DATA. 


occur in a natural state, while the latter are pioducts of the electric furnace, 
are very much harder and have greater cutting power and durability. 
Carborundum (SiC) is composed of 30% Carbon+70% Silicon Alundum 
is obtained principally from bauxite, an amorphous hydrate of alumina. 

Speeds. Peripheral speeds of wheels vary from 3,000 to i ,000 ft. 
per min., usually from 5,000 to 6,000. Cylindrical work in grinding- 
machines should have a peripheral speed of from 25 to 80 ft. per nun., 
the slower speeds for delicate work. The traverse speed of wheel = face 
of wheel X 0.75 per rev. of piece being ground. Polishing wheels should 
have a peripheral speed of about 7,000 it. per min. 

Grades of Wheels for Various Uses. Abrasives are classified (accord¬ 
ing to the size of their grains) by numbers which indicate the meshes 
per linear inch of the screen through which the crushed substance has 

1 a The cutting capacity of the various sizes compared with files is as follows: 
16 to 30, rough files; 30 to 40, bastard; 46 to 60, second-cut; 70 to 80, 
smooth-cut; 90 and upwards, suoerfine to dead-smooth. 

The Norton Emery Wheel Co. gives the following table which is approxi¬ 
mately correct for ordinary conditions. (/ = medium soft wheel, M — 
medium, Q = medium hard; other letters indicate corresponding inter¬ 
mediate grades): 

No. of grain. 


Large C. I. and steel castings (Q, R ). 12 to -0 

Large malleable and chilled iron castings ( Q , R ). 16 to 20 

Small castings (C. I., steel' and malleable iron), drop-forgings 

(P, Q) . 20 to 30 

W. I., bronze castings, plow points (P , Q), brass castings (O, P) . 16 to 30 
Planer and paper-cutter knives (/, K), lathe and planer tools (N , O) 30 to 40 

General machine work (O, P). . .... 30 to 40 

Wood-working tools, saws, twist-drills, hand-ground ( M, N ). ... 36 to 60 
Machine grinding: twist drills (K, M), reamers, taps, milling 

cutters (H, K) .. 40 to 60 

Hand grinding: reamers, taps, milling cutters ( N , P) . 46 to 100 

For grinding machines, the Landis Tool Co. gives the following: 


Material. No. of grain. Grade of wheel. 

Soft steel, ordinary shafts. 24 to 60 Medium or one grade harder. 

“ “ tubing or light shafts... 24“ 60 One or two grades softer than 

medium. . 

Hard steel and C. 1. 24 “ 60 Medium or one grade softer. 

Internal grinding. 30 “ 60 “ to several grades 

softer^-- 


Economy in Finishing Cylindrical Work is obtained by reducing 
stock by means of rough, heavy cuts to within .01 to .025 in. of the finished 
diameter and then grinding to completion. It is possible to force wheels 
to remove 1 cu. in. per min. 

Emery Wheels vs. Filing and Chipping. The figures in the follow¬ 
ing table express approximately the number of lbs. removed per hour 
by the various processes. The metal bars ground were f in.X£ in., held 
against wheel by a pressure of about 100 lbs. per sq. in. (T. Dunkin Paret, 
Jour. Franklin Inst., 5-12-1904): 



Brass. 

C. I. 

W. I. 

Hardened 
Saw Steel. 

Emery wheel. 

34. 

15.5 

5. 

6.87 

File. 

1 . 

.72 

.34 

. 125 

Cold chisel. 

2.56 

4.69 

1.31 

.187 

Wheel wear. 

.8 

1.37 

1.69 

3.63 


Grindstones for tool-dressing should have a peripheral speed between 
600 and 900 ft. per min. Rapid grinding speeds should not exceed 2,800 
ft ner min. 

High-Speed Tool Steel. In 1900 the Bethlehem Steel Co. exhibited 
tool steel at the Paris Exposition made and treated according to the Taylor- 
White natents. This steel was capable of taking heavy cuts at abnormally 
high cutting speeds, the chips coming off at a red heat, and the tool stand- 















HIGH-SPEED TOOL STEEL. 


123 


ing up well under the work. Since that date many steels of similar capacity 
have been placed on the market by various makers. 

These steels are air-hardening and contain (in addition to carbon) one 
or more of the elements, chromium, tungsten, vanadium, molybdenum, 
and manganese, these elements uniting with the carbon to form carbides. 
Iron carbides exist generally in an unhardened state and at high tem¬ 
peratures these part with their carbon, which then shows a greater affinity 
for chromium, etc. These newly formed carbides may be fixed by rapid 
cooling, and they impart the extraordinary hardness which they possess 
to the steel. This hardness is retained by the steel, as these carbides are 
not affected by changes of temperature within certain limits. Tools 
made from these steels are forged at a bright red heat and slowly cooled. 
The points are then reheated to a white, melting heat (about 2,000° F.), 
cooled to a red heat in an air-blast, and then slowly cooled, or quenched 
in oil. 

Cutting Speeds for High-Speed Tool Steels. Experiments have 
been conducted in Germany and also in England (by Dr. Nicholson of 
Manchester) to determine the best cutting speeds to employ on various 
metals, and the results are expressed by the following formula: Cutting 

speed in feet per minute, S — ■— —=-+M, where a is the sectional area of 

a + L 

cut in sq. in. (= depth Xtraverse in one rev.), and K, L, M are con¬ 
stants: 



Whitworth Fluid (Manchester) 



W. I. 


Pressed Steel 




Soft. 

Medium. Hard. 

Soft. 

Medium. Hard. 


K 

= 1.95 

1.85 1.03 

3.1 

1.65 1.3 

2.62' 

L 

= 0.011 

0.016 0.16 

0.025 

0.03 0.035 

0.0092 

M 

= 15 

6 4 

8 

7 5.5 

23.5 


Siemens-Martin Steel (Berlin). 
Soft. Medium. Hard. 

Cast Iron. Cast Steel. 

K 

= 4.03 

0.918 

1.17 

0.196 

0.2 

L 

= 0.012 

0.009 

0.0075 

-0.0199 

-0.005 

M 

= -26 

16 

20 

32.2 

11.25 


The chemical composition of the metals experimented upon is as follows: 


CAST IRON. 

Berlin. ,-Manchester. 






Soft. Medium. 

Hard. 

Carbon, combined. 


0.45 


0 

.459 

0.585 

1.15 

Graphite. 


3.46 


2 

.603 

2.72 

1.875 

Si. 


2.05 


3 

.01 

1.703 

1.789 

Mn. . .. 


1 


1 

.18 

0.588 

0.348 

S. 


0.1 


0 

.031 

0.061 

0.1614 

P. 


0.1 


0 

.773 

0.526 

0.732 

Crushing strength in tons of 2,240 lbs. 

26.9 

44 

43.5 



STEEL. 






Siemens-Martin. 



Whit wort h. 


Soft. 

Medium. 

Hard. 


Soft. 

Medium 

. Hard. 

Carbon. 

0.3 

0.54 

0.63 


0.198 

0.275 

0.514 

Si. 

0.05 

.21 

.20 


. 055 

.086 

.111 

Mn. 

.58 

.93 

1.22 


. 605 

.65 

.792 

S. 

.05 

.025 

.05 


.026 

.037 

. 033 

P. 

.07 

.05 

.05 


.035 

.043 

.037 

Tensile strength in 








tons (2,240 lbs.). 

26 to 32 

40 

* 49 


26 

29 

47 


Turning. The following results have been taken from the exhaustive 
presidential address delivered before the A. S. M. E., December, 1906, 


















124 




SHOP DATA. 


by Mr. F. W. 


and embody the practical conclusions of an investigation 
Tnvlor extending over some twelve years. • dl 

Tool’s U S ed round nose. For blunt tools radius of point width 

Si i jSiT andC. “Medium 

and soft steel). 


Depth 
of Cut 
in 

Ins. 

Feed 

in 

Ins. 

Cutting Speed in Feet per Minute for a Tool which is to 
last 90 Minutes before Regnnding. 

Soft Cast Iron. 

Soft Steel. 

Sizes of Standard Tools. 

Sizes of Standard Tools. 


lx in. 

1 in. ! 

J in. 

-1 in. 

It in. 1 1 in. 

f in. 

£ in. 

3 3 5 

T6 

TUJ 

1 

ft 

239 

191 

142 

118 

103 

85.0 

226 

177 

130 

107 

92.8 

75.7 

222 

169 

120 

97.0 

83.4 

66.4; 

206 

147 

97.5 

76.0 

64.1 

518 

366 

257 

209 

490 

339 

235 

189 

482 

323 

217 

172 

510 

322 

203 

I 

lit 

■h 

iV 

t 

A 

216 

172 

128 

107 

93.4 

76.8 

205 

160 

118 

97.0 

84.2 

68.6 

203 
156 
110 
88.8| 
76.2 
60.9i 

194 

138 

93.1 

72.1 
41.8 

450 
317 
223 
182 . 
157 

427 

296 

205 

165 

142 

423 

284 

190 

151 

128 

445 

281 

177 

135 

-is 

A 

3*2 

T3 

i 

A 

187 

149 

111 

92.5 

73.1 

66.4 

181 

142 

104 

85.8 

74.3 

60.6 

181 1 
137 
97.7 
78.0 
67.5 
54.2 

. 

182 

128 

86.1 

67.4 

370 

260 

183 

149 

129 

105 

358 

247 

171 

138 

118 

95.0 

358 

240 

161 

127 

404 

255 

161 

X 

4 

3^ 

A 

I 

3 

16 

168 

134 

99.8 

83.2 

72.6 

59.7 

165 
129 
94.3 
77.8 
67.5 
55.0 

167 

126 

90.8 

72.7 

62.7 

173 

122 

81.9 

322 

227 

159 

130 

112 

91.4 

315 

218 

150 

121 

104 

320 

215 

144 

359 

226 

I 

3^ 

T2 

A 

A 

i 

A 

144 

115 

85.1 

70.9 

62.0 

51.0 

143 

112 

81.9 

67.6 

58.6 
57.5 

150 
113 
81.0 
65.5 


264 

186 

131 

107 

92.2 

263 

182 

126 

101 

276 

185 

330 

1 

2 

3*4 

^2 

lV 

I 

16 

131 

105 

77.6 

64.7 
56.6 
46.5 

132 

104 

75.8 

62.6 

54.2 

44.2 



230 

162 

114 

92.6 

232 

161 

111 



3 

4 

3*i 

3*2 

* 

iftf 

1 

A 

112 

89.2 

66.2 

55.2 

48.2 
39.'J 

Speed for , „ „ „ _ _ 

Hard Cast Iron = 0.29 X Speed for Soft C. I. 
Medium “ “ =0.5 X “ “ 

Hard Steel =0.23X steel 

Medium “ =0.5 X. 


(Condensed from Tables 143— 154, Vol. 28, Proc. A. fe. M. E.) 









































































































































HIGH-SPEED TOOL STEEL. 


125 


„ Aver a ge composition of tool-steel: 0.3% V + 18% W + 5 76<2, Cr 4 - 
C + 0.09% , Mn + 0.046% Si. Fogged aT lighS yelljw i.eai! 

Hard steel (locomotive tire): 0.64% C + 0.7% Mn + 

nmit - 70 non iv. 44 7o p ' Tensi i e stre ngth= 118,500 lbs. per sq. in. Elastic 
!' ^o ^ Per cent - stretch = 14. Medium steel: 0.34% 

V T °' 6 3 fian 1 + °^ 3% OA fi + 0.032% S + 0.035% P. T. S.= 72,830® 

A J ii' ,°A™ tch , = 30%: contraction= 48.7%. Soft steel: 0.22% C 
+ 0.42 Mn + 0.07% Si + 0.025% S + 0.022 P. T. S.= 56,250; E. L% 
2o.>.)0, stretch—3o.o%: contraction*: 56.3%. 

Pressures on Cutting Tools, p, in lbs. per sq. in. 

Cast Iron: soft, 115.000; medium, 188,000; hard 184 000 

„ soft ’ 2 58 - 000 ; medium, 242,000; hard, 336,000.' 

Metal Removed in Unit Time. 

Cast Iron: lbs. per min. = 3.13 Sa; lbs. per hour =187.8 Sa. 

Steel: lbs. per inin. = 3.4 Sa; lbs. per hour = 204 Sa. 

Power Required by Cutting Tools (lathes, planers, shapers, boring 

l s) ir S‘ P ’ ~ 2*^-33,000 For nulling machines J. J. Flather states 
that 14.P. = cw, where w = lbs. removed per hour, and c = 0.1 for bronze, 
0.14 for C. I. and 0.3 tor steel. 

ilest Tool Angles. Dr. Nicholson indicates in his dynamometric 
experiments that the tool edge (in plan) should be at an angle of 45° to 
the center line of the work, the clearance from 5 to 6°, the tool angle about 
65 for medium steel (75° for C.I.) and the top-rake 20° for medium steel 
(9° for C.I.). (A. S. M. E., Chicago, 1904.) 

Average cutting stress: C.I., 150,000 lbs. per sq. in.; steel, 180,000 lbs 
H.P. = cutting stress X a X S = 33,000. 

Cutting H.P. for 1 lb. per min. = 1.46 for C.I. and 1.6 for steel. 

, H a P - losfc in toC)1 friction = 0.3 H.P. per lb. per min. .'.Gross H.P. = 1.76 
for C.I. and 1.9 for steel. 

The surfacing force for best shop angle (70° for steel) = 67,000 lbs. per 
sq. in. of cut; similarly, traversing force = 20,000 lbs. per sq. in. The 
surfacing force will thrust the saddle against the bed if the coefficient of 
friction equals or exceeds 0.333. The total net force to be overcome by 
the driving mechanism of the carriage for cutting steel = (67,000 X 0. 333) + 
20,000 = 42,333 lbs. per sq. in. of cut. Round -nose tools are preferably 
used. 

High-Speed Twist Drills. Power required oc r.p.m.; thrust oc feed per 
rev. Thrust increases more rapidly than the power consumed, consequently 
less power is required to drill a given hole in a given time by increasing 
the feed than by increasing the r.p.m. The angle of drill-point may be 
decreased to as low as 90° (standard angle = 118°), thereby reducing the 
thrust 25% and without affecting the durability of point. (W. W. Bird 
& II. P. Fairfield, A.S.M.E., Dec., 1904.) 

Metal-Cutting Circular Saws. Cutting cold metal: diam., 32 in.- 
thickness, 0.32 in.; width of teeth (cutting edge), 0.44 in.; teeth 0.2 to 
0.5 in. apart; circumferential velocity, 44 ft. per min.; feed, 0.005 to 
0.01 in. per sec. 

Cutting metal at red heat: diam., 32 to 40 in.; thickness, 0.12 to 0.16 in.; 
teeth 0.8 to 1.6 in. apart; depth of teeth, 0.4 to 0.8 in.; circumf. vel. 
12,000 to 20,000 ft. per min. (Ing. Taschenbuch). 

Taylor-Newbold Saw, with inserted teeth of high-speed steel: A 94- 
in. cold saw at 76 r.p.m. will cut through If in. hex. cold-rolled steel in 
26 seconds, and at 96 r.p.m., in 22 secs. A 36 in. saw, ^ in. thick, teeth 
averaging in. thick, running at a cutting speed of 85 ft. per min. will 
cut off a bar of 0.35 carbon steel 14 in. X8J in. in 20 min. A bar of 0.40 
carbon steel 5X5i can be cut in 4.4 min. 

Fits (Running, Force, Driving, Shrink, etc.). In the following table, 
which is derived from good practice, the first column gives the nominal 
diameter of hole. The mean value for each class of fit is given and also 
the permissible variation above or below same. For force, shrink, and 
driving fits the values given are those by which the diameter of the piece 
should exceed that of the hole, while for running and push fits they are 
the values by which the diameter of the hole should exceed that of the 
piece. Force and shrink fits are given the same value. Push fits are 
those in which the piece is forced to place by hand-pressure. Running 
fits are given three values: A, for easy fits on heavy machinery; B, for 
average high-speed shop practice; C , for fine tool work. 



126 


SHOP DATA 


Diam 
in in. 


0.5 

1 

2 

3 

4 

5 

6 


Force + 


Drive + 


Mean 


.75 

1.75 

3.5 

5.25 

7 

9 

11 


Var. 


.25 

.25 

.5 

.75 

1 

1 

1 


Mean 


.37 

.87 

1.25 

2 

2.5 
3 

3.5 


Var. 


. 12 
. 12 
.25 
.5 
5 
.5 
.5 


Push — 




A. 

Mean 

Var. 





Mean 

Var. 

.5 

. 12 

1.5 

.5 

.75 

.25 

2 

.75 

1. 25 

.25 

2.6 

.87 

1.75 

.25 

3. 1 

1. 1 

1.75 

.25 

3.8 

1.2 

2.25 

.25 

4.4 

1.4 

2.25 

.25 

5 

1.5 


Running — 


B. 


Mean 


1 

1.5 
1.9 
2.3 
2.7 
3. 1 

3.5 


Var. 


. 25 
.5 
. 62 
.8 
.85 
.9 


1 


Mean 


.6 

1 

1. 15 

1.5 

1.6 
1.87 
2 


Var. 


. 12 
.25 
.4 
.5 
.6 
.62 
.75 


The values above given are in thousandths of an inch ;i^in^diam^ Gt 
fit in a hole of 4 in. diam., the piece should be 4.0025 in. in diam. tit 
mav be either 4.002 in. or 4.003 in. and still be within the permissible 
variation of 0.0005 in. either way.) For locomotive^ Rresando^+ 
shrunk work. Allowance m thousandths of an inch —( I6 X diam. in m.) + 

°'°Siaes'^ove 6lln^DiamV: 19 For shrink fits add 0.0025 in. to diam. of 
piece for each inch of diam. of hole where the part containing the hoe is 
thick and unyielding. Where the metal around the hole is thin and elastic, 
add 0.0035 in. per in. of diam. For force fits multiply diam. of hole by 
1.0007 and add 0.004 in.; variation of 0.001 in is permissible. For dny* 
fits allow one half of the excess just given for force fits, tor running fits, 
multiply diam. of hole by 0.000125 add 0.00225 in. and subtract this 
sum from diam. of hole, thus giving diam. of piece. \ anation of 0.001 in. 
permissible. 

Power Required by Machinery. 

Machine. Material. No. of tools. H.P. working. H.P. light. 


Boring mills, 54 to 78 in. . . 
Slotting machines, 36X12 


C. I. 

2 

6 

1.5 

C. 1. 

1 

4.5 to 6.5 

2.5 

W. I. 

1 

5.3 & 7.3 

1.5 & 

W. I. 

2 

24.5 

5.8 

t t 

2 

12.5 

3 

4 4 

2 

16.8 

6 

t « 

2 in. drill 

2. 1 

1. 1 

4 4 

1 

7.3 

1.8 


PI onprc • 

Sellers, 62 in.X35 ft. . . 

“ '36 in. X12 ft. . . 

“ 56 in. X 24 ft- 

Radial drill, 42 in. 

Shaper, 19 in. stroke. 

(Baldwin Loco. Works; measurements by separate electric motors.) 

H.P. of motor required to operate 
under best conditions. 


Machine. 

Niles planer, 10 ft. X 10 ft. X20 ft. 

Pond “ 8 “ X 8 “ X 20 “- 

“ 5i “ X 5 “ X12 “ .... 

Gray “ 28 in.X32 in X6 ft. . . . . 

Gisholt turret lathe, 28 in. swing. ... . . 
W F. and J. Barnes drill press, 21 in . 
Niles radial drill, 60 in. arm 


30 
25 
15 

3 

4 
1 
2 

Emery Grinder, two 18-in. wheels in use, 950 r.p.m. ... 5 

Pond Vertical Boring Mill, 10-ft. table. 12 

Bement & Miles Slotter... . • 

Jones & Lamson Turret Lathe, 2 in.X24 in. 1, 

Gisholt Tool Grinder... 4 

Hendey-Norton Lathe, 16 in.. - 

Putnam Lathe, 18 in. 2. 

Pond 14 36 in... 10 

(F B. Duncan, Engineers’ Society of W. Pa.) 






















































COST OF POWER AND POWER PLANTS. 


127 


Punch and Shears, li-in. hole in 1-in. plate, 6 H.P.) 

shearing 1-in. plate, 15 II P. i 

Plate-edge Planer, 35 ft. X 1 in. 

15 ft. X £ in. . .. 

Wood Planers. 

Circular Saws.. 

(D. Selby Bigge.) 


Motor II .P. 


12 

30 

25 

4-16 

4-24 


n **• M otors for Machine Tools. Ordinary lathes: II.P.= 
o-too 1; Heavy lathes and boring mills under 30 in.: H.P. = 0 2345- 9 - 
Boring mdls over 30 in swing: H P =0.255-4; Ordinary drill presses:’ 
n on/ ^ ’ Heavy radial drills: H.P.—0.15; Milling machines: H.P.= 
Planers (2 tools), ordinary: H.P. = 0.25JT; Do., heavy; H.P.= 
0.41 W (Ratm of planer feed to return = l:3). Slotters: 10 in. stroke, 

stroke^ 5 il 3 p -6 5 tr ° ke ’ H ' P ==10; Shapers: 16_in - stroke, H.P. =3; 30 in 

• l u th ® above , 5 = iswing in inches and W = width between housings in 
inches, formulas based on the cutting by ordinary water-hardened 
steel tools at 20 ft. per min. (J. M. Barr, in Electric Club Journal.) 

It high-speed steels are used, the power required will be from 2.5 to 3 
times the above figures on account of increased speeds and cuts 

Power Absorbed by Shafting. In cotton and print mills about 25% 
ot the total transmission; in shops using heavy machinery, from 40 to 60%. 
In average machine-shops 1 H.P. is required for every three men employed*. 


COST OF POWER AND POWER PLANTS. 


, Cost ^ plant per H P - including dam, $60.00 to 
$100.00; without dam, $40.00 to $60.00. Power costs from $10 00 to 
$15.00 per year per H.P. 

St ea m Power. Cost of engines per H.P.- Simple, slide-valve, $7.00 
to $10.00; simple Corliss, $11.00 to $13.00; compound, slide-valve $12 00 
^A f ™? 0; a >ia°™ po V nd Corliss, $18.00 to $23.00; high-speed automatic, 
$10.00 to $13.00; low-speed automatic, $15.00 to $17.00. Plain tubular 
boilers, per H.P., $10.00 to $12.00; water-tube boilers per H.P., $15 00 
Pumps, $2.00 per H P. for non-condensing, and $4.00 for condensing. 
(Dr. Louis Bell in The Electrical Transmission of Power.”) Total cost 
of plant ranges from $50.00 to $75.00 per H.P., exclusive of buildings 

Dynamos and other electrical apparatus, including switch-boards, cost 
from $20.00 to $35.00 per kilowatt capacity ($15.00 to $26.00 per H P ) 
making the cost of an electrical power plant range from $65.00 to $100 00 
per H.P. 

The cost of a H.P. hour has been estimated by various authorities to 
range from 0.55 to 0.85 cents. Dr. Bell places it at 0.8 to 1.00 cent with 
large, compound-condensing engines, and at 1.5 to 2.5 cents with simple 
engines, basing his calculations on a day of 10 hours, under full load. If 
the load is fractional and irregular, these figures should be altered to 1.00 
to 1.5 cents and to 3 and 4 cents, respectively. 

I he cost of electric power includes the cost of steam power to operate 
the generators, interest, repairs and depreciation on the apparatus, attend¬ 
ance, etc. In very large power plants under good load conditions the cost 
per kilowatt hour (1.34 H.P. hour) may be as low as one cent, at the bus 
bars. 

Gas Power. The cost of plant is about the same as that of a steam 
plant. The gas consumption per brake H.P. per hour is about as follows- 
Natural gas, 10 to 12 cu. ft.; coal gas, 16 to 22 cu. ft.; producer gas, 9(j 
cu. ft.; blast-furnace gas, 116 cu. ft Coal consumption when producer 
gas is used is about 1.25. lbs. per B.H.P. With dollar gas, 1 B.H.P. costs 
2 cts. per hour. One B.H.P. in a gasoline engine costs about i.5 cents 
per hour, in an oil-engine about 1.75 cts. per hour, and in a Diesel engine 
from 1 to 2 cents, according to the cost of oil in the locality. 







128 


SHOP DATA. 


ProDortions of Parts in a Series of Machines. When two sizes of a 
machine have been constructed and it is desired to extend the 
to introduce intermediate sizes, the following method of Dr. Coleman 
Sellers may be employed: 

Let D be the larger nominal dimension, say 30 (of a 30-in. swing lathe) 

“ Dy “ “ smaller “ 12 C L2 ' m - ‘ 

Let diam. of lead-screw on D = C = 3 in., and diam of lead-screw on 

Dl = c, = 1.5 in. Thn D — D x = 30 -12 = 18 and C - CV-3 - 1.5.ih-JL 
C = 5-3- 18 = 0.0833= A, a factor. AD X — 0.0833 X 12-1. 

C.—AD, = 1.5 — 1 =0.5 = /, the increment. 

Let it be desired to find C 2 when D 2 = 20 in. Then 

C 2 = (D 2 XA) + / = (20X0.0833)+ 0.5 = 2.16 in. 

Hoisting Engines. Theoretical H.P. .required =•weight in lbs (of 
cace rope and load) Xspeed in ft. per min.-^33,000. Add 25 to bU A, 
fo? actual H.P. on account of friction and contingencies. Max. limit 01 

rope length in ft. x = where / is the breaking strength of rope in 

lbs. per sq. in., w = lbs. per foot of rope, D = dead weight to be lifted, in 

lbs., £incl 7 = factor of safety* - • i* m i erv i..-. ft • 

Elevators. Speeds: low, 0 to 150 ft. per mm.; medium, 150 to 350 It., 

high, 350 to 800 ft. Counterweights should be about 75% « f the weight 
Tckr and plunger. Floor area, 20 to 40 sq ft ^mber of elevators 
for a high office building = (Height of building in -ft. X330) % s P|jd m 
ft. per min. Xinterval between elevators m seconds). (C. W. JNistle, 

^ Wiref ropes for’ elevators (6 strands, each of 19 wires): Safe working 

load in lbs. = 11,600d 2 — 720,000^ (for Swedish iron); = 23,200d 2 -760,000-^ 

(for cast steel), where d = diam. of rope in in. and D = diam. of sheave in in. 
(Capt. H. C. Newcomer, U. S. A., F. N., 1 15.03.) 

Conveyor Belts. Lbs. conveyed per min.13,8-4, lbs. per 
hour = b 2 wV -3-230.4; tons per hour = b 2 wV + 460,800, whereat — width of 
belt in in., F = speed in ft. per min., w = lbs m 1 cu. ft. of the substance 
conveyed. These values are for flat belts; for trough belts multiply by 3 
Average F = 300; higher speeds may be used, up to 4o0 for level and 650 
when elevating at an angle. Approx. H.P. required to operate-lbs. per 

"^Electric 1 Cranes*.*' An’electric travelling crane consists of a bridge, or 
girder, a trolley running on the bridge and a hoist attached to the trolley, 
fach part being operated by its own motor. The following data are from 
a paper by S. S. Wales, read before the Engineers .Society of W. Pa. 

L = working load on crane, in tons; IF = weight erf bridge, mi tans. 
id = weight of trolley, in tons; £ = speed in feet per mm., P and Pi 
tractive force in lbs. per ton. 

% -Bridge.-• ' Trolley. ' 

Span. IF. P. L. uk ^ >1 * 

25 ft. 0.37, |0 1b f . jjt? ° gfr 

?g •• 1.0L 40 " 75 150 “ .5 L 40 “ 

100 “ 1.5L 45 “ 

H.P for bridge = P*8(L + TF + w)-3-33,000. (Use motor 1.5 times as large.) 
HP for trolley = Pi S(L + w)-i- 33,000 ( *-25 . 

H.P. for hoist =LS = 10( = 1 H.P. per ton lifted 10 ft. in one minute). 

Speeds in Feet per Minute (Ing. Taschenbuch). 

5 tons. 25 tons. 50 tons. 100 tons. 

■pr^ct 14 to 28 10 to 12 6 to7.5 5 

. 180 ° 300 140 “ 210 130 “ 200 120 

Trolley.’.'.'. .80 “ 120 50 “ 75 35 “ 55 25 to 35 












miscellaneous. 


129 


Paint and Painting. 

One gallon of linseed oil plus 40 lbs. of white lead will cover 250 to 
3o0 sq. ft of outside work with a good first coat. The same quantity 
w . second-coat and finish from 350 to 450 sq. ft. White lead when used 
on inside work turns blackish-yellow on account of exposure to the sufphur- 
ous fumes from gas or coal. White zinc is accordingly preferable for inside 
work, but, having less opacity, more coats are required. 

lor iron- and steel-work red lead (40 lbs. per gal. of oil) is an expensive 
durable covering. To prevent blistering on outside work boiled oil 
s oufa be used. Turpentine only should be used for thinning. Knots and 
pitchy surfaces on wood should be coated with shellac varnish, and all 
grease, scale, acid, and moisture should be removed from metal work 
before painting. Uraphite mixed with linseed oil and laid on in fairly 
thick coats makes a good _ paint for metals. Iron pipes, stacks, boiler 
fronts, etc., are varnished with asphaltum thinned with turpentine. 


ELECTROTECHNICS. 


ELECTRIC CURRENTS. 


Resistance (symbol R) is that property of a material which opposes 
the flow of an electric current through it. The unit of measurement is 
the ohm which is a resistance equal to that of a column of pure mercury 
at 0° C., ’of uniform cross-section, 1J6.3 centimeters in length and weighing 

1 lectro-inotive Force (symbol E, abbreviation E.M.F.) is the electric 
nressure which forces a current through a resistance. The unit of rneas ■ 
irement is the volt, the value of which is derived from the standard Clark 
cell whose E.M.F. at 15° C. is 1-434 volts. 

Current (/) An E.M.F. aoplied to a resistance will cause a flow of 
electricity which is termed a current. The unit of measurement is the 
nmnere or the current which flows through a resistance of one ohm when 
it is subiected to an E.M.F. of one volt. One ampere is the amount of current 
reauired to electrolvtically deposit 0.001118 gram of silver in one second. 
Ouantity (Q). The quantity of electricity passing through a given 
^ J r _ 1 A- ,, — mAnonrAil in nnnlnmK« OflG COUlOmt) 


cross-section of conductor h measured in coulombs. 


is 


the Quantity of electricity which flows past a given cross-section of a con¬ 
ductor in one second, there being a current of one ampere in the conductor. 

Capacity (C ) is that property of a material by virtue of which it is 
able to receive and store up (as a condenser) a certain charge of electricity. 
A condenser of unit ca-acity is one that will be charged to a potential 
of one volt by a quantity of one coulomb. The unit, of capacity is the 
farad which is too large for convenient use,—the microfarad (one millionth 
of one farad) being employed in practice. ... , 

Electric Energy (IF), or the work performed in a circuit through 
which a current flows, is measured by a unit called the joule. One joule 
is equal to the work done by the flow of one ampere through one ohm 

for one second. . . , 

Electric Power (P) is measured m watts. One watt is equal to the 
work done at the rate of one joule per second. One H.P. =746 watts. 
One watt = 0.7373 ft.-lbs. per sec., =0.0009477 B.T.U. per sec. One 
kilowatt = 1,000 watts = 1.3405 H.P 

Subdivisions and Multiples of Units are expressed bv the use of 
the following prefixes. One-millionth, micro; one-thousandth, milli; one 
million, meg-a, one thousand, kilo (e.g., microhms, microfarads, milli- 
amperes, megohms, megavolts, kilowatts etc.). , 

Aids to a Conception of Electrical Magnitudes. One ohm=resist¬ 
ance of 1 600 ft. of No. 8 copper wire (i in. diam.) approx., = resistance 
of 400 ft. of No. 14 copper wire (tb in. diam.) approx. One volt =90% 
of the E.M F. of a Daniell cell (Zn, Cu, and a solution of copper sulphate), 
66% of the E.M.F. of a Leclanche cell (carbon-zinc telephone battery), 

aP A 2*000 candle-power (c -p ) direct current arc lamp has a current of 
about 10 amperes flowing through it, and an E.M.F between the carbons 
oi about 45 volts; it consequently requires 450 watts of electric power. 

130 



ELECTRIC CURRENTS. 


131 


An ordinary 16 c.-p. incandescent lamp on a 110-volt circuit requires about 
0.5 ampere, its resistance being about 220 ohms and its power consumption 
about 55 watts. 

Ohm’s Law. If E is the difference of potential (E.M.F.) in volts between 
two points in a conductor through which a steady, direct current of 1 
amperes is flowing, and the resistance of the conductor between the two 

points is R ohms, then I or E = IR. 

it 

Divided Circuits. If a current arrives at a point where several paths 
are open to its flow.it divides itself inversely as the resistances of these 
paths, or directly as their respective conductances. (The conductance of 

a circuit is the reciprocal of its resistance, or :io : i 3 = — ; — • JL 

, . . . „ R ' n ro r? 

etc., and + i 2 + 1 3 = /. 


The total conductance of the branched circuits, -^=—+ —+—, etc and 
n . ' R r\ r 2 r 3 '' 

the reciprocal of this value equals the joint resistance of the several paths. 

For two branches =—-|-, and R = ~ r ' V2 - 

R n r 2 n + r 2 

Tvirclioff’s Laws. 1 . The sum of the products of the currents and 
resistances in all the branches forming a closed circuit equals the sum 
of all the electrical pressures in the same circuit, or IE = I(IR). 2. At 
every joint in a circuit, 27=-0. or the sum of the currents flowing toward 
the joint equals the sum of the currents flowing away therefrom 
Resistance of Conductors. The resistance R (in ohms) of a con¬ 
ductor of length l (in cms.) and cross-section s (in sq. cms.) is R = cl-t-s, 
where c is the specific resistance of the material (the resistance between 
two opposite faces of a cube 1 cm. long and 1 sq. cm. cross-section) 
Specific Resistances at 0° C. are given in the following table. When 
any higher temperature is taken, add as a correction b X clegs. C. above 


Specific re¬ 
sistance in b. 
microhms. 


Silver. 

... 1.468 

0.004 

Copper. 

... 1.561 

. 00428 

Gold. 

... 2.197 

.00327 

Aluminum. . . 

... 2.665 

.00435 

Zinc. 

... 5.751 

.00406 

Iron. 

... 9.065 

.00625 

Platinum. . . . 

. . . 10.917 

.003669 


Specific re¬ 
sistance in b. 
microhms. 

Nickel. 12.323 0.00622 

Tin. 13.048 .0044 

Lead. 24.38 .00411 

Mercury. 94. 07 . 00072 

German silver. . . 29.982 .000273 

Carbon. 4,200 to —0.2 

40,000 


Dilute Sulphuric Acid. 

Per cent wt. of H 2 S0 4 in solution . . 5 15 30 45 60 80 

Sp. res. at 18° C. in ohms. 4.8 1.9 1.4 1.7 2.7 9.9 

(For each deg. C. rise in temp, subtract 1.4% from above values.) 

Joule’s Law. If a current of I amperes flows through a resistance of 

R ohms for t seconds, the heat developed, = l 2 Rt, in joules or watt-seconds 
= 0.23 9I 2 Rt gram-calories, =0.0009477 1 2 Rt B.T.U 

The heat developed is equivalent to the energy causing the current 
flow. Rate of expenditure of energy, in watts, = El = I 2 R. Energy in 
joules or watt-seconds = Elt = I 2 Rt. 

Electrolysis is the separation of a chemical compound into its con¬ 
stituent elements by means of an electric current. Two plates or poles 
(electrodes) are inserted in the compound or electrolyte, the electrode 
of higher potential being called the anode, and the other the cathode. The 
products of the decomposition are called ions. A current / amperes 
flowing through an electrolytic bath will deposit a weight of G grams in 
t units of time. 

G=kalt, where a is the chemical equivalent of the substance. 

If t is in seconds, k =0.000010386; if t is in minutes, k=0. 0006232, 
and if t is in hours, /c=0.03739. The electro-chemical equivalent=grums 
per coulomb. 
















132 


ELECTROTECHNICS 


Grams 

Grams per per 
coulomb. amp. 

hour. 


Grams 

Grams per per 
coulomb. amp. 

hour. 


Aluminum 9 
Copper. ... 31.6 

Gold.65.4 

Lead.103 . 2 

Mercury. . . 99.9 
Nickel. . . . 29.3 
Nitrogen. . 4. 6 


0.00009347 0.3365 
.00032320 1. 1815 
.00087924 2. 4453 
.00107184 3.8585 
. 00103756 3.7352 ! 
. 00030431 1.0955 
. 00004840 0. 1742 ! 


Oxygen. . . 8 

Platinum. .97.2 
Potassium. 39 

Silver.107.7 

Tin.58.7 

Zinc. 32.4 


0. 00008309 0. 2991 
.00100952 3.6343 
. 00040505 1*. 4582 
. 00111857 4. 0269 
. 00060966 2. 1948 
. 00033651 1.2114 


(To obtain pounds per ampere-hour, multiply grams per ampere-hour 
by 0.0022046.) 


ELECTRO-MAGNETIS3I. 


Lines of Force. When a current starts to flow in a conductor, whirls 
of magnetism are generated around the conductor which seem to spring 
from its center, and the region so filled with these whirls increases radially 
in extent as the current increases, remains constant when a steady current 
is attained, and snrinks radially to nil when the current is interrupted. 

If the conductor is bent into a loop, an elementary electro-magnet is 

___ formed, with a pole on either side of the 

plane of the loop. If the conductor be 
wound into a number of loops along the 
'sjf'v surface of a cylinder, a Solenoid is formed 
■ and the whirls so add themselves together 

-v that they may be considered as loops, 

entering the solenoid at ail points of the 
» section at one end, passing along inside 
-XVj-—A*' parallel to the axis of the solenoid to the 

*- v *■“ " other end, thence emerging and returning 

outside in curved paths to the point 
Fig. 27. first considered (Fig. 27). 

These loops are termed lines of force, and their number depends on the 
number of spirals of conductor in the solenoid and the number of amperes 
of current flowing through them, or, as it is expressed, by the number of 
ampere-turns. 

The Intensity of the Magnetic Field (3C) at any point is measured 
by the force it exerts on a unit magnetic pole, the unit intensity, there¬ 
fore, being that which acts with a force of one dyne upon a unit pole, 
or one line of force per sq. cm. (A dyne is the force which, acting 
for one second upon a mass of one gram, imparts a velocity of one centi¬ 
meter per second.) 

Magneto-motive Force (if) is the magnetizing force of an electric 
current flowing in a coil or solenoid and is usually stated in ampere-turns, 
cy =4^,7-*-10 = 1.257n/, where n is the number of turns or loops of the 
conductor and I the current in amperes. The unit for is called the 
gilbert and is equal to 0.7958 ampere-turns. 

The Intensity of the Magnetizing Force per unit length of solenoid 
(3C) = 4 Ttnl -t-L = 1.257 a/ -r-L, where L=length in cm. If Li=length in 
inches, 3C =0 495n/-s-Li or, if expressed in lines persq. in., 5Ci =3.193n/ -r-L\. 

* Magnetic Induction (®) is the magnetic flux or the number of 
lines of force per unit area of cross-section, the area at every point, being 
normal to the direction of the flux. ® = /z3C, where /t is the permeability. 
The unit is the gauss, or one maxwell per normal sq. cm. 

The Magnetic Flux (</>) is equal to the average field intensity Xarea. 
The unit is the maxwell, or the flux due to unit magneto-motive force 
(M.M.F.) when the reluctance is one oersted. 

Reluctance ((R) is the resistance offered to the magnetic flux by the 
material undergoing magnetization. The unit is the oersted, or the re¬ 
sistance offered by one cubic centimeter of vacuum. 

Magnetic Susceptibility, (k) = -f-3C. 


* B, F, and H are commonly used in place of (B, ff, and 3C. 













ELECTRO-MAGNETISM. 


133 


Reluctivity (v) is the reluctance per unit of length and unit cross- 
section, = l-s- ,-e. Maxwells = gilberts-j-oersteds. 

Hysteresis. When a magnetic substance (e.g., iron) is magnetized, 
the intensity of magnetization does not increase as rapidly as does the 
magnetizing force, but lags behind it. This tendency is termed hysteresis, 
and it may be considered as an internal magnetic friction of the molecules 
of the substance. Continued rapid magnetizing and demagnetizing will 
cause the substance to become heated. Hysteresis ( h) may be calcu¬ 
lated by the following formula due to Steinmetz: h (in watts) = ry(B 1 - 6 A-nlO~ 7 , 
where k = volume in cu. cms. and n = number of complete cycles of mag¬ 
netization and demagnetization per second. 


Very thin, soft sheet iron. . .. 

* * soft iron wire. 

Thin sheet iron (good) 

Thick “ “ . 

Ordinary sheet iron. 


0.0015 
.002 
.003 
. 0033 
.004 


Soft, annealed cast steel. 

“ machine steel. 

Cast steel. 

Cast iron. 

Hardened cast steel. 


V- 

0. 008 
.0094 
.012 
.016 
.025 


The 3Iagnetic Circuit. Magnetism may be considered as flowing in 
a magnetic circuit in the same manner as an electric current does in a 
conductor and the following relation holds: 

,, Magneto-motive Force .... . , ^ 

Magnetic 4 lux =--, which is analogous to Cur- 


E.M.F. 


Reluctance 


Resistance" 

<J> = 3-r-6 1. Reluctance, (R = Z-s- pa, where Z = length of magnetic circuit, 
a=area of cross-section and p — permeability (see Dynamos). <P=5-r-(R, 

5 = 1.257 nl; nl =-=0.7958#—, where l is in cms. and a in 

pa-h 1.257 pa 

sq. cms. When and a, are in inch measure, nl = 0.3132f/>Zi = pa-,. 

Induction. If a conductor, of length dl, is moved in a magnetic field 
(of strength 3C) with a velocity, v (the conductor making the angle a 
with the direction of the lines of force and the direction of motion being at 
the angle d with the plane passing through the conductor in the direction 
of the lines of force), the induced electromotive force, dE = SCv sin a sin ftdl, 


-/ 


or, E — 3Cv sin a sin lidl. When a = i?=90°, E is a maximum and is 


equal to 3CvZ10 8 volts, when v is stated in cms. per sec. and l in cms. 
The mean E.M.F. of the armature of a two-pole dynamo, E — 


volts, where d> is the total number of lines of force flowing between the 
pole-faces, n the number of active conductors on the armature, and N 

= r,p.m. In a series-wound multipolar dynamo, E = — ■ ^ ■ volts, 


and in a multiple-wound multipolar dynamo, E = </>jnV10 —8 -f-60, where 
</>i=no. of lines flowing between one pair of poles, and p = no. of pairs of 
poles. 

The Direction of Currents, Lines of Force, etc. The lines of force 
in a magnet or solenoid flow from the south pole to the north pole and 
return outside to the south pole. The north pole of a magnetic needle when 
brought near a magnet points in the direction of the lines of force. 

To determine the direction in which a current flows in a conductor, 
place a compass underneath it. If the north pole of the needle points 
away from the person holding compass (who is at one side of the con¬ 
ductor) the current is flowing to his right. 

To find the direction of a currept flowing in a coil, find the north pole 
by means of a compass, the north pole of which will be repelled by the 
north pole of the coil or magnet. Then place the right hand on the coil 
with the thumb (at right angles to the extended fingers) pointing in the 
direction of the north pole and the current will be flowing in the direction 
in which the fingers are pointing. If the direction of current is known, 
the north pole may be similarly determined. 

The positive (+) pole of a generator of electric current is the one from 
which the current flows into the external circuit. . In primary batteries 
the zinc is negative, copper, carbon, etc., being the positive poles. 














134 


ELECTROTECHNICS. 


Direction of an Induced Current.—If the letter N be drawn on the 
face of a north pole and a conductor (parallel to the vertical lines of the 
letter) be moved past the pole in a plane parallel to the pole face, the 
direction of current flow will be determined by the motion of the point 
of intersection (projected) of the conductor and the oblique line in the 
letter N. Thus, if the conductor moves from left to right, the point of 
intersection moves from above to below, which indicates the direction of 
the induced current. 


ELECTRO-MAGNETS. 

Traction or Lifting: Power. If a bar of iron be bent into the shape 
of the letter U and coils of insulated wire are wound upon the limbs, the 
electro-magnet thus formed (when a current is flowing through the coils) 
will have a lifting or holding power on each limb of P (in lbs.) =B 2 a-i- 
72,134,000, where B = no. of lines of force per sq. in. of iron section and 
a is the area of one pole-face of the magnet. The number of ampere- 



where l is the length of the magnetic circuit in inches and //the permea¬ 
bility. B may be taken at 110,000 for W. I. and mild steel. . _ 

The above formula is used when the keeper or armature is in contact 
with the pole-faces. If the keeper (by which the weight to be lifted or 
held is supported) is distant z inches from the pole-faces, then, nI = 2zXB 
X 0 3133. 

If the iron is of good quality and far from saturation the number of 
ampere-turns required to force the flux through the metal part of the 
circuit is small enough, comparatively, to be negligible, and the formula 
value, which is the ampere-turns required to force the flux across the air- 
gaps, may be taken as the total. 


A 



An iron-clad magnet which may be similarly considered is shown by 
the part ABC in Fig. 28; the cylindrical core C, however, should extend 
through the coil to the plane AB. 

Plunger Electro-Magnets. Fig. 28 shows an electro-magnet of the 
iron-clad or jacketed type, which is provided with a movable plunger or 
core, D, an inner projecting core, C, and a guide or “stuffing-box,” E. 
The air-gap is indicated by z and x is the stroke of the plunger or its range 
of motion, which must be less than z in order to meet the conditions imposed 
in designing for certain specified pulls at the beginning and end of stroke 
Pull in lbs. =P = aB 2 -r-72,134,000 (1). R = n/-=-0.3133a (2). Maxi¬ 
mum pull (at end of stroke) = Pg. Minimum pull (at beginning of stroke) = 

Pi. Let y = Pg + Pi = j£ 2 , then ^y and B l ^Bg^-^ / y' (3). At 




































































































































electro-magnets. 135 


S, 0 fe ning , of stroke, RizXO.3133 —n/, and, at the end of stroke, 
0.3133Zj(/(z — x) = nl, consequently 

= Brj-i- Bi = '/y and z = x\Zy +Vy~ 1(4). 


Let d = diam. of core in in., then, a = 0.7354d 2 , and, from (1 ),d = 
9,580 vPi-i-Bi (5), which determines d if S/ is fixed upon. 

If d is fixed, Bi = 9,580'/Pi = d (5a). i rom (2), nl = 3,000z'/pl+d (6) 
which allows the calculation of the am; er -turns if d has been decided’ 
upon. Length of winding bobbin in in.=L; available winding depth in 
in - = T; mean length of one turn in in. = 3/; sectional area of coil in sq. in. = 
LT; winding volume = MLT. If the actual permissib'e current density 
over the gross section is 0, then nI = 0LT, or, LT = nI-h0 (7) For 
momentary work 0 may be from 2,000 to 3,000 amperes, if the magnet 
is well ventilated and provided with radiating surfaces. For continuous 
use over_several hours, /? = 300 to 400 amp. From (6) and (7), T = 

3,000 p/Pi + 0dL. Assume that L = z, then, if 0 is taken at 2,000, T = 

LSY^Pj-r-d ( 9 ). M = ff(0.25 + cf+ T) (10), assuming that the core of 
bobbin and clearance add 0.25 in. to d. Current density in copper (amperes 
per sq. in.) = a; diam. of bare wire = <J, do. of insulated wire= di ; R = 
resistance in ohms; r\ = resistance in ohms per inch of wire; s = sectional 
area of wire in sq. in.; a = space factor, = total copper section -hLT; V = 
volts at terminals; w = watts used; VI = I 2 R. ^ = resistance in ’ohms 
per cu. in. of coil space. If / is given, nl-±l = n; 0 = nl-r-LT ■ n = 
0.8a,9-r-(/ 2 X 10 6 ); s = I=a, and V = w-r-I. 

If V is gi ven. I = w = V ; r x = V + Mnl, or, R perl, 000 ft. = 12,000 V + Mnl 
d =0.001'/Mnl-T- F; s = 0.8Afra/-r- VX 10 6 ; a = 0.7854 < J 2 -v-^ 1 2 ; LT = ns-i-a, 
and M = 417dw-r-az'/Pi. 

If a solenoid is provided with an ample and well fitting iron guide or 
stuffing-box at the end at which the plunger enters the coil, the effect of 
its presence will be to bring up the field at the point when the plunger 
is just entering to the intensity which exists at mid-length of the solenoid 
The maximum pull (when plunger has reached the bottom of the coil) 
is one-quarter of that calculated from equation (1). If the permeability 
of the iron is known, B can be found from tables. 

Calculation of a Plunger Electro-Magnet. A number of designs 
should be made and the calculations tabulated in order to determine the 
most economical one, in weight of copper and in watts required. 

Example: It is required to design an iron-clad coil to give an initial 
pull of 25 lbs., increasing to 100 lbs. at the end of a stroke or range of 
2 inches, E.M.F. supplied being 100_volts. for intermittent work. 

P{/ = 100; Pi = 25; x = 2; y = 4; ' / y = 2; z = 4; ^P t = 5. nld = 3.000X 
4X5 = 60,000; Bid = 9,580 X5 = 47,900, and R^ = 47,900X2 = 95,800. 


d in inches.= 1 

nl .= 60,000 

Bi .= 47,900 

B .= 95,800 


Trial Values. 


2 3 

30,000 20,000 

23,950 15,966 

47,900 31,932 


4 

15,000 

11,975 

23,950 


Let /? = 2,000, <7 = 0.5; then, « = 4,000. Then, for T =<3 in. (which 
will allow from 10,000 to 30,000 amp.-turns per inch length of coil, if 
properly ventilated) 


d in inches.= 1 2 3 4 

LT .= 30 15 10 7.5 

L . = 10 5 4 3.75 

T . = 3 3 2 5 2 

M. . .’.’.'.'.’ .’.’ .* = 13. 36 16. 5 18.' 07 19.65 

MLT .= 400.8 247.5 180.7 147.4 

8 .= .09 .07 .06 .0543 

s. = .006413 .00396 .00289 .002357 

/.= 25.65 15.84 11.56 9.428 

n.= 2339 1894 1730 1591 

v .= 2565 1584 1156 942.8 

Copper, lbs. ..... = 63.73 39.35 28.73 23,44 





















136 


electhotechnics. 


If it is desired to use metric units (1) should read: Pull in kilograms- 
dJ 24 655000 and (2). R = n/ = 0.795*, where B us the .flux density m 

LiiwK 

following formulas, which are due to C. R. Underhill (E. W. * ylL- ’ 

„/.[10.000P-«P-P t )] + P.'., A-O.oWnl; ,i-0.1128'vV; where 
P —null in lbs on 1 sq. in. of plunger section when nl — 10,000, A & e f 
of section ^nsq in and & = an empirically determined factor. P c and k 
are to be determined from the following formulas which have been dernred 

+°of pl Un ier 

( *S SSt£g‘\Vw%To°fdSirSi. and the range through which it 
will be practically uniform will —O.oL. , ftY1 , 10=5X2 = 

Exa T le = For a pull »»*. H ta f 'd£l.523 %. 

From an examination of ’the data employed by Mr. Underhill the ^mpiler 
has deduced the following formula, which is much simpler and sufficiently 
accurate: nI — 99P(L + 1). 


CONTINUOUS-CURRENT DYNAMOS. 


Connections and Flow of Current. Series-wound dynamo: Arma¬ 
ture-field magnets—external circuit—armature. 

, , . , < field magnets 1_armature 

Shunt-wound dynamo • Armature— { externa i circuit > armatuie. 

Compound-wound dynamo, short shunt: 

. , (series magnet coils external circuit Lw_ arma ture. 

Armature | shunt magnet coils 

Compound-wound dynamo, long shunt. 


Armature- 


series coils— I e ? cterna ^ c ^ rc ^ t ., } —armature, 
series cons j shunt magnet coils > 


(In the brackets the current divides between the paths in the upper 
and lower lines inversely as their respective resistances.) 

Efficiencies of Dynamos. Let E = E.M.F. m volts; / armature 
current in amperes; e = volts at terminals of dynamo; t = amperes in ex- 
ternal circuit ; is — amperes in shunt coils; El -total watts;. «-useful 
watts in external circuit; = armature resistance; ii! 2 = series-coil re¬ 
sistance- Ri = shunt-coil resistance; r = resistance of external circuit 
(all resistances in ohms). N = r.p.m.; * = electrical efficiency = n + EI; 

commercial efficiency = ei+ 746X H.P. Then for magneto and sepa¬ 
rately excited dynamos, y. = e-*-E = r+(r + R 1 y,for series-wound dynamos, 
_ = e _i. E = r + (r + Ri + R 2 )', for shunt-wound machines, jj e = ei-r-hl- 
X + (h r + i s 2 Rt + I 2 R 1 ) ; for compound-wound, short-shunt dynamos, 
Ve J e i + EI = i 2 r +mr + R 2 )+i8 2 R 3 + I 2 Ri] I „ for compound-wound, long- 
shunt dynamos, r, f = ei = El = i 2 r - 1 - [Pr + I 2 (Ri + R?) + i8 2 R 3 l _ 

The Armature. Let ni = number of coils on armature and n 2 — number 
of turns per coil; then, the number of active conductors for anng armature, 
nn = n,n 2 ,—for a drum armature, n 0 = 2n!n 2 . Ihe E.M.F. — <f>n o sl0 - • 60, 
where s is the number of revolutions per minute. The cross-section of 
the armature iron, « = * + £, where R = 10,000 to 16,000 lines per sq cm. 
(65,000 to 100,000 lines per sq. in.) for soft charcoal-iron discs, the lower 


CONTlNUuUS CURRENT DYNAMOS. 


137 


of't'hes^valie.s!) 150 ^ 1 ' machines - ^ For th « air-gaps take only about 40% 

2 500(n/^^uVn °— f 7 fpf iH ng Fa,)p states that , B should equal or exceed 
(u )07 n f \ .• ’ ^ ^h>] for ring armatures (for drum armatures take 

turns rLTSred where «>> is the ““mber °< ampere 

luim'bor of hi n m, T e the reluctance of the air-gap, and ( nl) 2 is the 
iik back ampere-turns of the armature. [(n/) 2 = no of conductors 
included by one pole-face Xcurrent strength in amperes. a ctors 

of thf in . the aima ture sets up a magnetization opposed to that 

of the field magnets, and the effective field is the resultant of the two. 

The external diam. of armature. d e = k$/EI + m (J. Fisscher-Hinnen) 
v here ), length of armature = </ e . For ring armatures z. = n r ...i 
is in cm. and =4.6> when d e is in inches; >1 = 0.5 to 1.4. N = r.p m For 
dnim armatures A;-10 ( d e in cm.), and =4 ( d e in in.); >1 = 0.75 to 2 8 

and h f03 to'n°fiV/ 0 f!” f mature d ‘ sc ’ *-(0.7 to 0.8)rf e for ring armatures 
and (0.3 to 0.G)d e for drum armatures. The peripheral speed s should 

* ^ c % d , p . er sec - ( 15 meters) for small armatures, ’and 80 ft 

100 ft irl f f F a f ge ar , ma , t > ires - ( In exceptional cases it may reach 
iuu it. per sec. as for steam turbine generators.) 

The length of an armature, l, =(1.05 to 1.2)^-^-. for smooth-surfaced 

thlPfeetlf’ 4'he r e t ro° the<1 f arma f U >f ’ <h is the dia meter at the bottom of 

bv alfowinir 000 to Knrf C - . ° f t o e armatlire conductors is determined 
allowing 600 to 800 circular mils per ampere. To find the diameters 

wires tt0n ' C ° Vered WireS ’ add the followin S values to the diameters of bare 


Gauge. 

0 to 10 
10 “ 18 

18 and upwards 


Single- 
covered. 
0.007 in. 
.005 “ 
.004 “ 


Double- 

covered. 

0. 014 in. 
.01 “ 
.008 “ 


me\al°( 0 e 0 r A 0 t a o V 0 09 e r[ k S C + U u rre J\ ts armatures .are made up of discs of sheet 
(0 015 to 0.0-5 in. thick) which are insulated from each other bv 
sheets of tissue-paper, rust, or by japanning their surfaces. A sheet o^f 
good insulating paper-board is inserted at about every half inch of length 
Th° P ? n SI - aCeS are l eft fbout every two inches to provide for ventilation, 
the loss in watts due to eddy currents = ( 14.5 to 16.5) Xk(Btv) 2 X 10~i 4 
where k — cu. cm. of iron in the core, t = thickness of discs in mm. and 
p = no. ot periods per sec. 

Armatures, when adequately ventilated in order to avoid injurious heat¬ 
ing, and running at peripheral speeds of from 30 to 50 ft. per sec., require 

.o ° , 7 h S t T- }°- 7 l *° 108 sq - in -> o' ex,ern “' from Xch 

tomdiate the heat of each watt wasted therein. (Kapp.) 

Ihe permissible rise in temperature (40° to 50° C or 75° to Q0° F 1 

sY+no^Y + Xindeis F.) -ilLsVi 8 

*5(1 + 0.0305s), where TF = watts lost in armature, *S’ = outside surface of 
armature in sq. in. and s = peripheral speed in ft. per sec. 

. , order to avoid fluctuations of E.M.F. and the sparking due to self- 
induction, the number of coils on the armature should never be less than 
50, and as much larger as is consistent with the design The EMF 
between two consecutive segments of the commutator should not exceed 
(45-0.2/) volts for currents under 100 amperes, and 20 to 25 volts for 
hea.'v let currents. Hie radial depth of the windings on an armature should 
not exceed one-tenth of the core diam. so that the distance between the 
core and the pole-faces may be as small as possible. The core should 
be well insulated from the windings by means of press-board, canvas etc 
in driving the armature, each conductor opposes the motion bv a re¬ 
sistance, or drag, F (in kilograms) = (8/ = 9.81 X 10 6 , where / = length 
of conductor in cm., and B = induction per sq. cm. F, lbs. =78/= 11 303 COO 
v'here l is in inches and 8 in lines per sq. in. / = current in amperes') ’ ’ 

the wires should therefore be secured against motion relative to the 
core surface. In small armatures the frictional resistance of the wind¬ 
ings is sufficient, and in toothed armatures the teeth provide backing for 
the wires. Ihe coils must also be held in place against the action of een- 



138 


ELECTROTECHNICS. 


trifugal force by bands of Corman silver ^^^olu^ion? secured 

^between 

through the armature core theie ■ tQ be cons idered as a closed 

magnet cores, and yoke) the line. t j = 0.7958<P(R. If l is 

for iron! n/^O.7958///, where 5 j^+g. ^ JJ^ t %jLm, 
i.e G , f H' 0 ^ 1 the^nimbe 1 ? ?f V impe?e-turns ^eq^rld^o forced lines through 
1 cm. length of iron. 


Ampere-turns for 1 

- B. - 


per sq. cm. 

2,000 
4,000 
6,000 
7,000 
8,000 
9,000 
10,000 
11,000 
12,000 
13,000 
14,000 
15,000 
16,000 
17,000 
18,000 


per sq. in. 

12,900 
25,800 
38,700 
45,150 
51,600 
58,050 
64,500 
70,950 
77,400 
83,850 
90,300 
96,750 
103,200 
109,650 
116,100 


cm. length of mean path of lines of force (H'). 

I 

Sheet metal. Cast steel. W. I 


0.35 
.75 
1.1 
1.25 

1.4 
1.6 
1.75 
2 

2.7 

4 

6.5 
12 
21 
40 
71 


0.65 
1.3 
2 . 1 
2.65 
3.25 

4 

5 

6.5 

8.6 
12 
18 

26.8 

40.6 

58 

93 


.0.5 

1 

1.7 

2 

2.35 

2.8 

3.4 

4 

5 
7 

12 

21 

40 

72 

120 


C. I. 

3 

6.5 

18 

31 

48 

72 

97 

133 

176 

232 


iSSt tnTMMpt d °vSL S 

in table by 2.54. The value of ,u may be found from table, it being equal 

t0 For^high densities such as are found in the teeth of sheet-metal armature 
discs, 


B per sq. cm.— ^’?Rn 

//' per cm.= 100 


20,000 

184 


21,000 

320 


22,000 

800 


23,000 

1,450 


peculation of the Ampere-turns of a Dynamo. Armature: <0 a , 

, C andR 7 are determined by the design of the armature;/„ is approximately 
measured from the dimensions of the core discs, and, the ' alue o 

C °If e tEe n armltme 1 s toThedfa^peraal calculation is necessary; a, is then 
the erofsSon of the iron in the teeth before one pole-face and should 

area that A is about armature core 

to noifree- ‘^-i 6 . where’l 2 d I are respectiyelyjhe length of the 
arcand the breadth of the pole-faces. B^-fP^ • a air ana (n/) mr 

1 - Eipld-—Not all of the flux in the field magnets passes through the arma- 
h d, n„V Inst through leakage between the poles. This stray 

ture, a pa A m 50 % of the total flux and the field flux must 

fhUtcm’Te accordingly greater than that required by the armature. 
The nSSber of lSSs of foref in the field, Vm-cK, where c has the following 

values: 





CONTINUOUS-CURRENT DYNAMOS. 


139 


Types of Field Magnets. 


Same,—yoke at bottom . . . ’ c = 
Vertical double magnet (Man- 


Capacities of Dynamos in Kilowatts. 



1 


10 

100 

300 

500 

1,000 

2,000 

1 

.65 

1 

.45 

1.3 

1 

. 2 





1. 

45 

1 

.28 

1.2 








8 

1 

.55 

1. 4 







1 

.5 

1 

.32 

1.25 

1. 

2 

1. 18 

1. 16 

1. 

15 

1. 

4 

1 

.3 

1.22 

1. 

18 

1. 15 

1. 12 

1. 

i 

2 


1 

.7 

1.55 

1. 

45 

1. 4 

1.35 

1. 

3 


The sectional area, am, is calculated in accordance with the permissible 
which for C.T. is from 5,000 to 10,000 lines ner sq. cm ('32.000 to 04 000 
rwr so. in), and for W I. and steel is from 10 000 to 16 000 oer so Vm 
(65 000 to 103,000 per sq. in.). Then, (n/)m = KWm 

If the cores yoke, and pole-pieces are of different materials, a separate" 
calculation of the ( nl) for each should be made and their sum taken. On 
account of the reaction of the armature current upon the field the 
latter is weakened and it is therefore necessary to add from 7 to 15% 
to the number of ampere-turns, 4 his amount may be approximately 
calculated by the following formula of Kapp: Let g = the shortest distance 
between two pole-pieces; then, (nl)g = n 0 Ig~ x{d e + 2d), where « 0 = No of 
active conductors on the armature, d e = external diam. of armature in cm 
and 8 = air-gap between armature core and pole-face in cm. 

Finally, the total number of ampere-turns required in the field magnets 
nl = (nl ) a + (n/)air + ( nl)m + ( nl)g = 

In series machines im = I or a fractional part thereof. In shunt machines 
im is determined by the loss permissible in the coils for excitation The 
mean length of one turn L m (in meters) is previously calculated- the 
resistance, r m is calculated with regard to the permissible drop, em, and 
The cross-section of the magnet wire in sq. mm. is then 
<*w = Lmnl -T-55em. 

The current density in the field coils should not exceed 2 amperes per 
sq. mm. (1,300 amp. per sq. in.). In shunt machines from 20 to 40% of 
the field resistance is used for regulation. 

Kapp states that from 10 to 16 sq. cm. of outside coil surface (1 5 to 
2.5 sq. in.) is necessary to radiate the heat of each watt lost in the coils 
The rise in temperature (25° to 35° C.) t (C°) = (280 to 320) W h- surface in 
sq. cm. = (43.4 to 49.6) W -5-surface in sq. in. Also, f(F.) = (78 to 89 )IF-t- 
surface in sq. in. TF = No. of watts. 

Fields should be massive, compactly designed with well fitted joints 
and in large sizes should be of W. I. or steel as C. I. requires too great a 
weight of copper. A circular section should be preferably adopted, sharp 
edges and corners being avoided, as they tend to increase the leakage. 
Sparking may be decreased by so boring and adjusting the pole-pieces 
that the tips are farther distant from the armature-core than art the 
points midway between the tips. 

Eddy currents in pole-pieces may be avoided by slitting the faces in 
planes at right angles to the axis of rotation of armature, or by construct¬ 
ing the pole-pieces of sheet-iron laminations. 


The Commutator segments should be from 0.25 to 0.4 in. thick, made 
of cast or hard-drawn copper, and insulated from each other by’thick¬ 
nesses of from 0.025 to 0.04 in. of mica. The segments should" have a 
length of about 1.25 in. for each 100 amperes of current, when copper 
brushes are used. _ When carbon brushes are employed, length should 
be from 1.8 to 2.5 in. per 100 amperes. 

Brushes. Copper brushes should have a surface of contact with the 
commutator of from 0.0055 to 0.007 sq. in. per ampere, brass brushes 
from 0.008 to 0.01 sq. in. per ampere and carbon brushes froom 0.018 to 
0.038 sq. in. per ampere. Each brush should cover about 1.5 segments 
and should be from 1.5 to 2 in. in width, excepting in small machines, 
where lesser widths are used. 


Armature Shafts should possess unusual st iffness in order that vibra¬ 
tion may be avoided. Diam., d = cA^/H.P. -h N, where c = 16 to 23 when 
d is in cm. and 6.3 to 9 when d is in inches. 

The Weight of a Continuous-Current Dynamo in lbs.=386/v$, 
where K = output in kilowatts at 1,000 r.p.m. (Fisscher-Hinnen). About 







140 


ELECTROTECHNICS. 


abridged from assenes °J articles b;^ ap J, illustration of the methods 
(London, Jan. to July, 19114; a nous-current generators. A 400- 

em ployed in the designlarge — 8 pdes (100 r.p.m.) is 
kilowatt machine (5o0 \olt, - x 10~ 8 (1). where T = no. of 

taken as an example E.MJ.-4JM * » ^ N = cycles per sec. 
armature turns in series between + ana ^ core) M = magnetic flux 

or periodicity of _ reversals of flu- ™a a mu itiple-circuit wind- 

linked with coils in mature. The arma The exte rnal diam. 

ing, there being 8 paths through it for the^curre r Gross length of 

D = 230 cm. The polar pita!h_ r-^ 230 Th * re ^ g ventilati ng ducts, 
■armature between flange g length is taken up by insulation, 

each 13 mm wide, and 10% of ^ he mea n length of one arma- 

Net length between flange n Tota l number of armature 

ture turn (lap winding )^ + 2^-3^7cm * r slot the total number of 
slots = 264, and, as there are 6 number G f turns = 1,5844-2 

face conductors = 264 X 6 - 1,584,^a the toita^ ^ g = 99 . Total length of 

= 792. Turns in series between o j tie_ _o 2 400 cm. Cross-section 
conducting circuit between brushes 327 * | 9 3 ’ Total C ross-section 

of one conductor = 2.4 mm.X13 mm.-U.^ ^2X8 = 2 5 sq. cm. Arma- 
between brushes (8 conductor^^g»g U 0 ^ 00 2 =2.5 = 0.026 ohm. Voltage 
ture resistance at “ So”SWxO 026 ohm = 19'voltB. Drop at brushes 

Jf *"■“ 

PS+ 2?:574°voTts. W =(100 + 60) X(8 4- 2)-6.67,and T -99; substituting 
these values in (1), M -21,800,000 lines. currentg . Watts per kilogram of 
Core loss due t? hysteresis and e ; . =100 (2). If the internal 

weight, = 2.54XperiodsXkilohnes per sq. cm. ( , 2Ctn2 _ 140 2 ) = 

diam. of armature disc = 140 cm., gross area of disc - 4 U30 0 ) 

26,100 sq. cm. Area of one slot (3 3 ; cm deepjX 1.23 cm. ™*>> rea 4 °« 

SQ. cm Area f^tstoo ^^cm v7lume° ofiron in core-25,000 X 

6 W, 000 00 cu. 2 c£.-5.250 kgs. The » » « 

the slots, consequentiy th ®J r a f if entei-s^he’eore and flows’ both to the 
but, as the field flux divides as it enters tjeoo ^ (jf core? and the 

left and right, twice this value, - - Q00 4 - 2,270 = 9 'h00 lines, or 9.6 

flux density in core will then be r 2 i’ f™ (2)^=2.54X 6.67X9.6 + 100 = 

l! 7 ,h oi e for the 6 S£t!re°cor e = 5,250 ^IZ^cyYmdM surface of armature: 

fq-Kp?n 

Surface = 7 rDL = jrX 230 X 104 / P’’ 72 A = 7 oa 2 x 0.026 = 13,100 watts, and 

the copper of armature conduct ^ ^00 watts. Watts per sq. dm. 

*=22,0(X) 750 ==29.4^ for whicl?value'the rise in temperature will not exceed 

3 °The M.M.F. corresponding to 

per cm. of length for sheet iron. ( . values for H' of American 

Kfgher than that gy P p r ^ E ar maWre pcf^pole = 42 cm. 42X4 

^if-M.M F. for armatu^core. 

Tooth density and pole, 

faC £ =6 / C ^vW22 21 lie below'the mean pole-arc. Allowing 10% for 
67% of „ wh / cb 2 -, 2) total number of teeth through which the flux passes 
“so-ead” pf flux the total ^ThA hottom of slots = 223 cm., and circum- 
= 24.4 Diam. of armature at the bottom ol siots = ^ boUom 

ference at same diam. = 7 00 cm 00 28 cm leaving width of tooth = 1 .43 
of slots. Width of slot is taken -1.23 cm., leading wiut „ fl4Q 
“ ,44 teethX 1 43 = 34.8 cm. at roots. 34.8XA n or Zl J4U sq. cm. 

Of magnetic circuit at roots of teeth for one pole, and the apparent 
flux density-2C800!000-940-.23,200 lines per sq. cm. This apparent 


CONTINUOUS-CURRENT DYNAMOS. 


141 


density must not be employed, but a corrected one which varies according 
to the ratio of the slot width (a) to the tooth width (b). In this case 
«-*-6 = 1.43 = 1.23 = 1.16, and by interpolating in the following table the 
corrected density is found to be 21,800 lines per sq. cm., requiring 640 
amp.-turns per cm., or, as length of tooth = 3.3 cm., 2,100 amp.-turns 
per coil for the teeth. 


Apparent 

Density. 



a = 6= 0.5 

18,000 

17,400 

20.000 

18,800 

22,000 

20,000 

24,000 

21,000 

26,000 

22,000 

28,000 

23,000 

30,000 

23.700 


Corrected Density. 


0.75 

1 

1.25 

17,700 

18,000 

18,300 

19,200 

19,500 

20,000 

20,400 

20,700 

21,300 

21,500 

22,000 

22,400 

22,600 

23,000 

23,400 

23,600 

24,000 

24,500 

24,600 

25,000 

25,500 


Air-space or gap: Area of pole-face = pole-arcXlg = 61 X40 = 2,440 sq. 
cm. Average pole-face density = 21,800,000-7-2,440 = 8,900 lines per sq. 
cm. Ampere-turns per coil =0.795Xaverage densityXlength of gap in 
cm. = 0.795 X 8,900 X0.9 = 6,400. 

Magnet cores and yoke: Cores may be of cast-steel, W. I., sheet metal, 
or C. I.; yokes of C. I. or cast steel,—occasionally of sheet metal. Densities 
for large machines are kept around 14,000 to 15,000 lines per sq. cm. for 
cast steel and at about 16,000 for W. I. In smaller machines low r er values 
are taken. The flux for the cores and yoke must be greater than that in 
the air-space and the armature (or account of leakage or dispersion of the 
lines of force when leaving the poles), and the armature flux must be 
therefore multiplied by a leakage factor, or, as it is called by Prof. S. P. 
Thompson, a dispersion coefficient, which ranges from 1.1 in very large 
machines to 1.25 in small and compactly designed ones. In this example 
it is taken at 1.13 and the flux in field is therefore 21,800,000X1.13 = 
24,600,000 lines. The core density is then 24,600,000 = 1,630 = 15,100 
lines for cast steel, the core being 45.5 cm. in diam. and having an area 
of 1.630 sq. cm. The yoke is of cast steel and is designed for 9,000 lines 
per sq. cm., and has therefore a total sectional area of 2,772 sq. cm., but 
as the flux divides after leaving the core and flows to the right and left, 
this value is seen to be twice the actual cross-section, which is 1,386 sq. cm. 

The length of the path of flux in the magnet core is 50 cm. and that for 
the yoke and pole-shoe is 73 cm. ( = £ of the total length of path in the 
yoke between two consecutive cores). The number of amp.-turns per cm. 
length of core at 15,100 lines = 28, and for total length of 50 cm. = 1,400 
amp.-turns. The amp.-turns per cm. of yoke length at 9,000 lines = 6 
or for total length of 73 cm. =440 amp.-turns. 

Total ampere-turns per coil for 574 volts, at no load. 


Armature core below the slots. 168 

“ teeth. 2,100 

Air-space. 6,400 

Magnet core. 1,400 

Yoke. 440 


Total 


10,508 


The direct demagnetizing effect of the armature winding when a current 
is flowing is very considerable and increases the more the brushes are 
displaced from the mechanical neutral point. This effect may be closely 
calculated from the formula: Amp.-turns per field coil to overcome demag¬ 
netizing component of the armature field =0.01757P7 7 a , where 7 = amperes 
per turn in armature coil, T a = armature turns per pole, and P = percentage 
of polar pitch by which the brushes are set in advance of the neutral point. 
In this example, 7 = 730 = 8 = 91 amp., T a = 99, and, if brushes are set 
ahead 15 segments of the commutator, P = 15X 100 = 99 = 15.2%, and 
0.01 75IPT,, = 2,400 amp.-turns. 

The distortional component of the field set up by the armature current 
may be taken at 10% of the total armature field per pole = 730 amp. X 










142 


ELECTROTECHNICS. 


99 turnsXO.lO-t-8-900 amp.-turns. Therefore for 550 terminal volts 
(574 volts internal) at full load are required: 

Amp.-turns for saturation at no load .. 

“ to counteract demagnetization. . . 4AUU 

* < “ “ distortion. ooU 

TotaJ . 13 308 per po * e 

(In a two-pole dynamo, if the brushes are set at the meohM^cal^utTal 
point^the'eiTect of'tto armature current is purely one °f dem^netisation 

3*3* aTtlte 

13 S; 9 ffoTor i h; 4 windX--(nVmatures with voltages up to 1 000 the 

croe^section. to™™™ 
C Tal1ulaSn W of°L^eS^Sp d a?| W fXtor taken at 0,5 for both coils. 

Tlm^engtlfailowable ^.^f^j^j^g^hig^eifgthf n^n^ortioift'fThe 

irFSi'Se^'oi, 8i M,« 

excitation is wasted 1 J r “‘^TfoWto! or OzTrmtts or each of the 

™d”K? %™‘f1 Im for clearance, the ii.ten.al diam. of coil-46 cm., 
8 coils. A.11C g , ,i , u a the external diam. will be 54 cm., 

and assuming radial <ieptJ ° b ‘* cm.^tfte^e: xx te g The watts per 

and the mean lengt l _ 0 0 ooi 76 ^ 2 -{-A, where fc = kgs. of copper per coil 

Sh TV-°i a n turns' per co 1 ( = 9,300). Cross-section of shunt coil = 

98V4-11? sa cm Which, multiplied by the space factor (0.5) = cross- 
28X4-114 sq. cm., * Cu cm . G f copper in coil = 

y iVx 100 = 8 900 and, as 1 cu.'cm. weighs 0.0089 kg the kgs. of 
?op X per 5 fn X one°shunt coil = 79. Substituting these values m above formula, 

1 h The & exterriaf^cyHndrical tamface of coil = 48 sq. dm., and. the watts per 
sq dm. therefore = 10, which allowance will not permit a rise in temperatuie 

° f sTze'o/wire In shunt coils :-Amps. per coil = watts - volts per,coil = 

fain 6? CroLcec«on per frn No. of tufa - 56 + 1,210 -0.0462 sq cm. 
l-“id- t ’ S r _ o4fi9 = 167 amp. per sq. cm. Diam. of bare 

wire re -2.42 e mm Watts in 8 colls-3,840. Watts in shunt rheostat-380. 

Total watts for e f areTdaced at the end"of core* nearest the armature. 
Senes eo.ls -These are pteed “ 4 «f 0 e a “ p.-turns + 730 amp.-6 turns. 
Winding length i- et . mn sre diverted through a shunt in 

<In !,t fTh'fhe^Tef winding a f P iha7 turn" -4.420 h- slo-8.5 ) The 
parallel with the hi her current density than the shunt coils, and, 

series coils may nave a g cm the cross-section of the series turns = 

730= S i'80 a =r05 sq cm. This may be in the shape of a rectangular section 






CONTINUOUS-CURRENT MOTORS. 


143 


(\ cm. X 1.01 cm.) and wound edgewise. Mean length of 1 turn = 158 cm 
Weight of copper in one coil = 6 turns X 158 X4.05 X0.0089 = 34.17 kgs., 
or 273.36 kg. for 8 coils. Resistance of 8 coils in series at 60° C. = 8 X 6 x' 
158 X 0.000002 -5-4.05 = 0.00374 ohm. 

Watts lost in the 8 coils, at 60° C. = 730 2 X0.00374 = 1 , 993 . 

Reactance voltageWhen a coil carrying a current arrives at and 
passes the brush, the direction of the current is suddenly reversed. This 
change should take place sparklessly and the winding should be so designed 
that the reactance voltage due to the decreasing current at the moment 
of commutation will be as small as possible at full load, the brushes being 

set at the neutral point. Reactance voltage = 12.566e (4+0.15 —) , 

where e = average voltage per coil ( = 550 = 99 = 5.5 volts), Q = amperes 

in conductors per cm. of periphery of armature ( X^~^ = 200 amp.), 

Vo 23(j7t / 

B = average flux density per sq. cm. of cylindrical surface of armature 
[ = (8 X 21,800,000) = (28 X 230 X n) = 8,600 lines], and r = \ n = ratio of polar 
pitch to net length of armature core ( = 99 = 27 = 1.49). 

The reactance voltage, consequently, is 2.42 volts for this machine, 
which is low enough to permit a practically sparkless commutation. The 
brushes should be held against the commutator by a pressure of about 0.1 
kg. per sq. cm., and the loss in watts due to brush friction = 0.1 kgX section 
of brushes in sq. cm. X0.3Xperipheral speed of commutator in meters 
per second X9.81, where 0.3=coeff. of friction for carbon brushes ( = 0.2 
for copper brushes). The current density in brushes ranges from 4 to 
12 amp. per sq. cm.,—average = 6 . 

The IE loss at commutator in watts = total armature currentXvolts 
dropped at brushes ( 1.2 to 2 . 8 ,—average, 2 ). 

Efficiency:—The following is a tabulation of the several losses of energy 
in the generator at full load: 


(а) Core loss in armature. 8,900 watts (constant) 

(б) I 2 R “ “ “ . 13,100 “ (variable) 

(c) Brush contact loss. 1 ; 460 “ “ 

( d ) Brush friction loss.. .. 540 “ (constant*) 

( e ) Friction loss at bearings, estimated. .. . 3,000 “ “ 

(/) Loss in shunt coils. 3,840 “ “ 

(a) “ series “ . 1,993 “ (variable) 


Total losses.. 32,833 watts 

Output = 730X550 = 401,500 watts. Total generated = 401,500+ 32,833 = 
434,333 watts. Efficiency at full load = 401,500 = 434,333 = 92.5%. At 
half-load, losses = a + d + e + / + 4(6 + c + g) = 24,560 watts. Output = 200,- 
750 watts, and total generated = 200,750+ 24,560 = 225,310 watts. Effi¬ 
ciency at half-load = 200,750 = 225,310 = 89%. 

Cost of manufacture: The factory cost of generators of this class is 
proportional to the product of the diameter of the armature by the “equiv¬ 
alent length of one armature turn over the end connections,” which latter 
may be taken = /!^ + 0.7r. The factory cost then = KD(Xg + 0.7x), A being 
a function of voltage and of the type of machine. For 6 and 8 pole dy¬ 
namos of 250 volts, K may be taken at $0.30, and for 500 volts at $0,265 
to $0.28. (These values are for material and labor costs and for methods 
of manufacture obtaining in England.) 

The output and speed being decided upon, a series of calculations should 
be made, the diameter of armature being so chosen that the peripheral 
speed will vary from 10 to 15 meters per sec. and the total ampere-turns 
per pole on the armature varying from 4,000 to 10,000. From these 
designs a choice may be made which will be the best compromise on such 
points as cost, speed, and reactance voltage, all of which should be as 
low as possible. 

For a two-circuit winding on a multipolar dynamo armature, where 
one pair of brushes is used, No. of face conductors = No. of poles X(wind¬ 
ing pitch ± 2 ). 

CONTINUOUS-CURRENT MOTORS. 

These are generally designed on the same lines as are dynamos of similar 
types. The revolutions of the armature develop an E.M.F. which is op- 













144 


ELECTROTECHNICS. 


posed to the impressed E.M.F. and which is called the counter electro¬ 
motive force. Let E = E.M.F. applied at the terminals of motor, e — 
counter E.M.F., and R = resistance of motor armature. Then, I = {E — c) 
- 5 - .ft; total watts, W = EI = E(E — e)-r-R; useful watts, w, — eI = e{E — e)s-R\ 
W = w + I 2 R (or watts lost in heating), and the efficiency=wv W — e-i-E. 

Torque = mechanical power in ft.-lbs. -h angular velocity. Let t» — 2nX 
revs, per sec. = angular velocity, T = torque; then, ( 6 T = mechanical power 
in ft.-lbs. per sec. e/ = electrical power of the armature in watts. H.P. = 

777 : =^- 77 ;,and el = 2 itnT X = 8,52n7 7 , where n — revs, per sec. e = nm(J> 10~ 8 , 

550 7 4b 550 

where m = No. of conductors on the periphery of armature and = flux. 
T at 1 ft. radius = md>I-i- (8.52X10 8 ). If r = resistance of armature, 

«> :...> T ... , ft,) = m *(®zi ! )-.(8.52X10*). R.p.m.-eX60 




and T (at 1 


X 10 8 -s-m 0 . 

Rheostats for Motors. If a motor at rest were directly connected 
to a source of current, the mains would be short-circuited through the 
armature and the abnormal current flowing would speedily burn up the 
armature coils. It is necessary, therefore, to introduce a starting resist¬ 
ance into the armature circuit so that only a moderate current will flow 
through the armature at the beginning of its motion. As the speed (and 
consequently the counter E.M.F.) increases, the current strength decreases, 
and the resistance may be lowered gradually, by steps, and when full speed 
is attained it may be cut out of the circuit altogether. The following table 
gives the resistance and current-carrying capacity of several metals used 
in rheostat coils: 



Galvanized Iron. 

German Silver; 

W.G. 

Ohms 
per ft. 

Arnp. 

Ohms 
per ft. 

Amp. 

8 

0.00266 

28 

0.00566 

19 

10 

.00366 

21 

.00833 

14 

12 

.006 

16 

. 0127 

11 

14 

.0117 

10 

. 0203 

7 

16 

.016 

7.5 

. 0333 

5 

18 

.029 

4.5 

. 0583 

3 

20 

.041 

3.5 

. 115 

2.2 

22 

.0883 

2 

. 18 

1.5 

24 

. 144 

1.5 

.29 

1 


Platinoid. 


Ohms 
per ft 

Amp. 

0.008 

13.5 

.0123 

10 

.019 

7.7 

. 032 

4.7 

.05 

3.5 

.089 

2.2 

158 

1.5 

.262 

. 95 

.423 

.7 


Man- 
ganin. 
Ohms 
per ft. 

0.0093 
.0133 
.021 
. 0363 
. 0553 
. 1013 
. 1446 
. 3133 
.5 


Resistance coils should be wound according to the following table, which 
gives the sizes for maximum rigidity and energy dissipation: 


B. W. G. 

Inner diam. of 

Approx, le 

Spiral in inches. 

Coil in in 

8 

1 

27 

9 to 11 

0.875 

22 

12 “ 14 

.75 

18 

15 “ 16 

.625 

14 

17 “ 19 

.5 

11 

20 “24 

.375 

8 


A starting resistance should be so designed that the momentary increase 
of current due to cutting out a section of same does not exceed a certain 
predetermined amount. 

1 2 3 4 n 

0 r 0 R\ 0 R 2 0 i ?3 0 — Rn —0 -Current flow. 


In the above diagram r is the armature resistance, ft lt ft.,, R 3 , R n are 
the sectional resistances of the rheostat included between the segments 
1, 2, 3, 4, n. Let the E.M.F. of supply = E; f = current in armature at 
full load; / = permissible momentary current, and let Is-i = k The re 
sistance R x between segments 1 and 2 should then be = (k — l)r, Ro = (k—l)kr 
R‘s = (k—l)k 2 r, and Rn = (k — l)k n ~ 1 r. ’ ’ ' 

In order for the motor to start, the total resistance in the circuit 
w~ r + + R 2 + R s . . . +Rn ) mist be less than E + i. To avoid arcing 

between the segments no sectim should have a drop of over 35 volts and 







ALTERNATING CURRENTS. 


145 


Uvo U o? more C lTtions U nnnfnf r ^ .^e calculation it should be divided into 
nore sections, none of which have a drop exceeding ‘t'y voltQ 

motors using about 50 amperes on full load / mly take ® a? equaU^ 
t+10 amp. For much smaller motors | for the first section and—t 

n"J (/-.Tthould noYex^dolf ° Urrent eXCeeds 30 amp ' the ““■"entary 

^iTS rteiat^Jir ° f . MS 

of each buffed S'l“Ss 

heostat is designed to start the motor, say on half-load, 7 = 25- I=z + ]0 = 

res'istLnca-8"s ohm^T?. 1 ' 4 "~ 58 ; 66 ’ and »" 12 'ections ' J-d-total 
values" 8 ’ 8 h The several sections would have the following 


Ri = (fc~l)r 
R 2 =Rik 
R3 — Rzk 

Ri = 

Rs = 
i?6 = 


0. 15 
= .06 
= .084 
= .1176 
. 1646 
.2305 
.3227 


ohm 


R 7 =0.4518 ohm 
Rs = .6325 “ 

R 9 = .8855 “ 

Rio = 1.2397 ohms 
flu =1.7355 “ 

^12 =2.4297 “ 


Total =8.5 


As n is a fraction over 12, the 
added to Rw. (Condensed from an 
April, 1904.) 


remaining 0.3 ohm (8.8-8.5) may be 
article by F. H. Davies, in Technics, 


ALTERNATING CURRENTS. 

^?'l niti0nS * 1 Alternating currents are those which periodical!v nass 
through a regular series ot changes both in magnitude and direction 
sually the magnitude increases with a certain regularity from zero to 
a maximum, decreases with the same regularity to zero and thensimfloJ,, 
to a maximum in the opposite direction and finally to’zJro aiain Whin 
a current has experienced such a series of changes (0 to +mSx Vo 0 

Thor max -' to 0 it is said to have completed one cycle. (Symbol i 

There are two alternations in one cycle The time taken tn ~ Y 

one cycle is called a period and ^numtar of 

second is called the frequency, or periodicity. The frequency if an alt?rna t 
jv-r.p™ d y nam °-^+60. where p-number o? paim of poles!™,] 

The ideal curve of an alternating current and E.M.F. is a sinusoid 
or curve of sines, and is the one assumed for purposes of theoreUcaf dis 
pressures. bUt commercial alternators do not generate strictly sinusoidal 

Referring to Fig. 29 E' at any point = F max . sin 2 nft, where / = frequencv 
a ™ =t i™ e Mi/ s f conds - Also, / = / max . sin 2 icft. ^uenc Y 

Values. One ampere of alternating current is a currenf 
Os such instantaneous value as to have the same heating effect in a con 
l UC / 2 °r T ° ne ampere of direct or continuous current Heating varies 
as 7- and, therefore, in an alternating current whose instantaneous 
vary, the heating effect is proportional to the mean of the squares of the 
instantaneous currents, or, P- = I m * + 2. The effective value therefore 
is 7-7m: v 2 and the effective E.M.F., E=E m +V 2 The avpis.ro 

current, 7 av . =2/m-*, and the average E.M.F., F av . ~2Ernt “ The 

ratio of the effective E.M.F., and the average F M F. = ^ 2Er n _ x ^ 

(for sinusoidal E.M.F.s) is called the form factor. (The subscript. ™ 
indicates maximum.) v e &uoscript m 

Phase. When the maximum and zero values of E and 7 occur at tho 
same instant, the current and E.M.F. are said to be in phase When 
the current attains its maximum and zero values at a time later than 
when the corresponding values of the E.M.F. occur, it is said to be out 






146 


EI ECTROTECHNICS. 


of phase with the E.M.F., or to lag behind the E.M.F. When maximum 
and zero values are reached at an earlier tune, the current is said to lead 
the E M F The distance between any two corresponding ordinates ol 
current and E.M.F. may be measured and expressed in degrees and is 
called the angular displacement, or phase difference. This angle is repre- 

An Alternator giving a single pressure wave of E.M.F. to a two-wire 
circuit is called a single-phase current generator. One giving pressure 
to two distinct circuits (each a single phase), the phases being 90 apart, 
is a two-phase, or quarter-phase generator. A three-phase macnine 



theoretically has three two-wire circuits, the maximum positive pressure 
on any one circuit being displaced from each of the pressures in the other 
two circuits by 120°, but, as the algebraic sum of the currents in all three 
circuits (if balanced) = 0, the three return wires of the circuits may be 
dispensed with. 

Power in Alternating-Current Circuits. The power, P, in an alter¬ 
nating circuit depends on E, /, and <£, and is thus expressed: P = EI cos <£. 
Cos 4> is called the power factor, it being the number by which the apparent 
power, or volt-amperes (EI), must be multiplied in order to obtain the 
true power. When E and / are in phase, <f> = 0 and cos<£ = l. 

Self-Induction Impedance, Reactance, and Inductance. A cur¬ 
rent flowing in a conductor sets up a magnetic field around it; conversely, 
when there is an increase or decrease of the number of lines of force cut 
by a conductor, a current is induced in it, and in alternating circuits it 
is necessary to consider these self-induced currents. 

When the rate of change of value of the current strength is greatest 
(at 0) the self-induced E.M.F. is a maximum, and when lowest (at peak 
of the sine curve) the E.M.F. is a minimum; consequently, the phase 
of the self-induced E.M.F. differs from that of the impressed E.M.F. by 
90°, or is at right angles to it. 

Let an alternating current of / amperes flow through a circuit having 
a resistance of R ohms and an inductance (self-induction) of L henrys. 
To maintain the current flow through R requires an effective E.M.F., 
E r = RI. The effective value of the E.M.F. of self-induction, Es, will 
be = —2 icfLI, the minus sign indicating that it is an opposed, or counter 
E.M.F. As E r and Es are at right angles to each other they are not to 
be added, but are to be taken as two sides of a triangle, the hypothenuse of 

which is the impressed E.M.F., E: whence, E = V E r 2 + E s 2 = 
v' (IR) 2 + (2 JifLI) 2 , and I = E + ^K* + (2xfL)*. \ / R^ + (2nfL) 2 is called the 











ALTERNATING CURRENTS. 147 


S,^'SeTi„ or „iZ p ,TFiL r io i ). tancc ’ aml (2 ' /L) “ ,e rcactance ' both boing 

,, f tbe part of the impressed E.M.F. which sends the current through 
the conductor (Ea being that required to neutralize the self induction) 
the current must be in phase with it, and 7 is therefore always displaced 
9 ° f rom f jS ‘, I an d E r lag behind E by an angle ($) whose cosine = F r -i- E 
<i> /hv- g 111 U u tanC fl ^ a °oil on the field of a generator is: L fin henrys) = 
f n w/ 19, » ^here <P is the total flux from one pole, n the number of turns 
in coil, and 7 the amperes of current in coil. 

Capacity. Any two conductors separated by a dielectric (i.e., insu- 
? a r ^ 0nstl ^ ut f a condenser. In practice this term applies 

sKaof CO f 10n of thin sheets of metal separated from each other bv thin 
sheets of insulation, every alternate sheet of metal being connected to 
?. ne 'e™™ 1 °/ tbe apparatus and the intervening leaves of metal to 
the other terminal. The function of a condenser is to store up electrical 

SSw'^a^%n t ,TT. E - M -^ *8 condenser, a Current nfll 

F°W’ large at first, but gradually diminishing until the metal sheets 
haAe been charged to an electrostatic difference of potential eaual and 
opposed to that of the E.M.F. applied. The capacity of a condenser is 
numerically equal to the quandty of electricity with which it must be 
charged in order to raise the difference of potential between its terminals 
from zero to unity. A condenser whose potential is raised 1 volt by the 
charge of 1 coulomb has a capacity of 1 farad. ^ 

The capacity in microfarads of a condenser = <7 = 0 . 000225 ——, where 
^= are ? °[ dielectric between two metal leaves, in sq. in.; n = number 
tteTapaly e if°u:e : fflT “ mib: ““uc- 



CM 

II 

ptf 



K 

CM 


II 

f4 


Fig. 30. 


Fig. 31. 


fin V 2 ^n S 2 ‘? 7 -° 7 : ? bon jte, 2.2 to 3; gutta-percha, 2.5; paraf- 

" if 2.3, shellac, «.75; mica, 6.6; beeswax, 1.8; kerosene, 2 to 2.5. 
If a sinusoidal E.M.h., E, of frequency, /, be impressed on a condenser, 

the latter will be charged in — seconds, discharged in the next seconds 

and charged and discharged in the opposite direction in equal succeeding 
intervals. Max. voltage, Em=Ey / . 2; max. quantity, Qm^-EC^Y; quan¬ 
tity per second =4fQm = 4fEC^ / 2 = average current, 7 av ., and, as the effective 
current, 7=^=-/ av ., 7 = 2nfCE, and ~7. is called the capacity 

reactance and is analogous to 2 n}L. 

Circuits containing Resistance and Capacity. In this case the im- 
pressed voltage, E must be considered as being made up of E r ,~which 
sends the current through the resistance, 7?,—and E„ which balances the 
counter pressure of the condenser and which is 90° in phase behind the 

current. E r = RI, and E c — *** I m P r essed E.M.F, E — E r 2 + E c 2 

T E 

or I ■ 




2 xfC 
(See Fig. 31.) 













148 


ELECTROTECHNICS. 


anCe = ——, and lags behind the current by 90°. These two E.M.I. s 
being 18(E C apart, the resultant reacta nce is their numeri cal difference and 

the general equation is: I = E-irVR 2 +[_^f^- 2 ~Jc\ ‘ The quantity 

within the brackets indicates an angle of 1^, if positive, and an angle 

.« , • Tf q tj -then I — —. This condition prevailing, 

of lead, if negative. If 2 ^ L - 2n fC' R ... 

•a one instant, energy is being stored in the 

rat Comi)taation! of'Condensed. If condensers are connected m series 
their combined capacity, C —- - - If Cu C2 ' " ' Cn afG 


_Cx_ 

n 


J_ + J_+JL 
Ci C 2 C 3 


1 ■ 

’ + Cn 


equal capacities, C v 

If connections are in multiple, C = Ci + C 2 + C 3 + . . . Cn, and if Ci-C 2 

“ SS .t^zWSprlLs t Was, p & 

ZS whosehorizontal ’sides repreSnt the resistances and vert.cal sides 
Hie reactances. The resultant impedance is then represented hy the 

hypothenuse of the triangle whose b a se = s , ur P of the! re ®i st fu Ge J^ctance 
tals of the separate triangles and whose height- sum of the reactance 

or admittances. 

Tak c anv two admittances at their proper phase angle and construct a 
naralleloeram The diagonal will be the resultant of these two admit- 
in'direction and value. This resultant.may bewmdariy ™mb,med 
wUh n third admittance, etc. The reciprocal ot the final resultant aamn 
tance will then be the combined impedance desired and the direction o 
the final diagonal will represent the resultant phase. 


alternating-current generators. 

Alternators are either single-phase or poly-phase (i.e., more than one 
u„ s „ —usually two or three). For low potentials the field is Hatio a \, 
the armature revolving, while for high potentials the field is made to 
mtate the armature being fixed. The latter may have a field of radial 
Doles each of which is of opposite polarity to its neighbor, or, it may be 
of the inductor type, in which both field and armature coils are stationary, 
the rotating part being an iron mass called the inductor This .inductor 
(which carries no wire) has pairs of soft-iron projections termed inductors 
which are magnetized bv the current flowing in a feed annular field coil 
which surrounds but does not touch the inductor The surrounding frame 
is provided with radial internal projections which correspond to the in¬ 
ductors in number and size, and upon which are wound the armature 
coils As the inductors revolve the flux linked with the armature coils 
varies from a maximum to a minimum, but its direction is not changed, 
as the annular field coil gives a constant direction of held. . 

Two-Phase Generator. In a two-phase system of winding, if t 
coils and 4 conductors are used, each coil generates a pressure of E \olt. 
between the two wires leading from it and there is no connection between 
the two coils. If three wares are used, connected as shown in Fig. 32 
the EM F.’s between the wires are as indicated in the diagram. (L and 
I in the figures are taken as the effective E.M.F.’s and currents.) . 

A monocyclic generator (for lights chiefly, but carrying a certain motor 
load) is a single-phase machine to which is added on the armature a so- 







ALTERNATING-CURRENT GENERATORS. 


140 


called “teazer” winding of a section sufficient to carry the motor load,- 
and with turns enough to produce a voltage equal to one-quarter of that 



Fig. 132. 


of the regular winding and lagging 90° behind same. One end of the 
teazer winding is connected to the middle of the regular winding and the 



other to a third line-wire. A three-terminal induction motor is used, 
which is either connected directly or through a transformer. 

Four-Phase, or Quarter-Phase. See bigs. 33 and 34 for the two 


















150 


'ELECTROTECHNICS 


stvles of connections. The current in each line in Fig. 33 — /, and in each 

line of Fig. 34 =/v / 2. , v 4t , ,, 

Three-Phase (Figs. 35 and 36). Fig. 35 shows the ^ or star con¬ 
nection, the current in each line being I. Fig. 36 shows the J (delta) 

or mesh connection, the current in each line being 1^3. 




E.M.F. Cenerated. E a . y = 2p(Dn — 10~ s , where p = number of pairs 

of poles, <P = flux per pole in maxwells, .V = r.p.m., and n = number of in¬ 
ductors. The effective E.M.F. = «L 7 aT , where k is the form factor ( = 1.11 
for a sine wave). Also, pN -i- 60 = f, consequently E = 2.22<Pnj\0 ~ 8 . 

If the armature winding is all concentrated into one slot per pole, single¬ 
phase, this formula is applicable. If, how r ever, the wires are distributed 
over the surface, of the armature in a number of slots the right-hand mem¬ 
ber of the equation must be multiplied by a distribution constant, Aq, 
which varies according to the number of slots on the periphery of arma¬ 
ture from center to center of two adjacent pole-faces and the fraction of 
the latter distance which is occupied by slots. 

Values of k\. 


Part of polar 


distance occu¬ 
pied by slots. 

1 slot. 

2 slots. 

3 slots. 

many slots. 

0. 1 

1.00 

0.996 

0.995 

0.994 

0.2 

1.00 

.986 

.984 

.982 

0.3 

1.00 

.972 

.967 

.962 

0.4 

1.00 

.95 

.942 

.935 

0.5 

1.00 

.925 

.912 

.9 


.. 









TRANSFORMERS. 


151 


TRANSFORMERS. 

I he transformer is a device for changing the voltage and current of 
an alternating electric system and consists of a pair of mutually inductive 
circuits (primary and secondary) or coils interlinked with a magnetic 
2!n U V; °n Cor ®- W hen . an alternating voltage is applied to the primary 
S?., a S alternating flux is set up in the iron core which induces an alternating 
in the secondary coil in direct proportion to the ratio of the number 
C)I r in rnS °* ^ • P( im ary and secondary coils. 

le magnetic circuit or core is made up from laminations of sheet iron 
or steel, two general types are used: I, the core type, which is built up 
trom laminations, each of which is a rectangle, with a similar but smaller 
rectangle stamped out from its center. These laminations are bound 
together with the holes corresponding and coils are wound on two opposite 
limbs. 11, the shell type, which is similarly assembled, but in which 
each lamination has two rectangular holes stamped out. The coils are 
wound on the central limb formed by the bridges or cross-pieces between 
tne rectangular holes in the laminations. Laminations are about 0.014 in. 
truck and are insulated from each other by shellac, tissue paper, etc., in 
mucn the same manner as are the discs in armature cores. (See Fig. 37 
the coils being wound on the limbs marked a.) 



I. II. 

!Fig.j37. 


Volts induced in transformer coil, £ = 4.447’. (P/IO -8 , where 7’ = total 
nU i?j f r °* ^ urns °f wire in series and / = frequency, in cycles per sec. 

Eddy current losses;—Watts per cu. cm. of core = (^/R) 2 10~ 16 , where 
t- thickness of each lamination in mils, and B is in lines per sq. cm. 

Amperes required to magnetize core to induction B =——— where 
. , , .... 1.76 uT’ 

l- length ot magnetic circuit in cm?., R = lines per sq. cm., 7’ = No, of 
turns in primary coil, and g = permeability of the iron in core. 

The current at no load 


i (magnetizing current) 2 + ( 


watts lost in iron 
primary voltage 



• r £ ra w Sf ? r E ler t Abridged from articles by Prof. Thos. Gray, 

in E. W. & E., April 23 and 30, 1904). • y ’ 

Let a, b, and l be the dimensions in cm. of the cross-section and mean 

length of the copper link or coil, and oj, b\, and l\ be similar dimensions 
for the iron link or core. Then, total cross-section of coils = a6 = A, and 
cross-section of core ~ci\b\ Volume of iron, and volume 

of coils, v = Al. (In this discussion the laminations are assumed to be 

rectangular and the wires as being bent sharply at right angles as they 

turn the corners of the core.) 

For a core transformer, ab = total section of both coils. I = 2 
(A. \ 

and li = 2\a + — + 2ax). In order that / may be a minimum (assuming 






































































152 


ELECTROTECHNICS. 


A, A\, and l\ to be constants and differentiating), it is found that for this 

a\ b — a , a bi—a x 
condition 7 — = r—— , and 77 — , , • 

b 1 b-f-a b oj+ai . - , 

For the least total volume of material in both cores and coils it is louna 


necessary that 
A\(A + 2.4j) 


a 


2 = 


A Aj 


6 2 = 


A(A+Ai) 






and 6 i 2 = 


A+A x ' “ ~ A x ’ A+2A!* 

If the volumes are to have a definite relative value, let 


v x = nv, and let the corresponding relative value of the areas be; A x -xA. 


Whpn r = 05 1 1.5 2 3 4 

* £-0.796 1.086 1.286 1.435 1.637 1.77 


5 

1.864 


Let the induction per sq. cm. of core = P sin wt, and the total induction 
A\B sin wt\ then, the magnetizing current being small, the amplitude ol 
the applied E.M.F. will (when the transformer is not loaded) be practically 
equal to that induced by self-induction; consequently, k —n\A\Bi»i\i , 
where rti = No. of turns on primary coil. 

Let P = full load in watts, / = square root of the mean square ot the 

full-load current in primary coil, and power factor =1. Then, P = EI — 2, 

or 1.41P = F7. Let t = average current per sq. cm. of coil section, me 
heat generated in the coils will then be, approximately, =4t idu , assum¬ 
ing the space factor of the coils is 50% (i.e.,^ one-half of coil section is 
copper), and the working temperature = 80° C. . , 

At full load the heat wasted in the coils should equal thawost m the 

core through hysteresis and eddy currents. This heat, H = in watts 

per cu, cm. per cycle per second. ,. 

A certain area of radiating surface, s, must be allowed for the dissipation 
of the heat of each watt, the total surface being S. For ordinary air¬ 
cooled transformers s is taken at 30 sq. cm., and at 20 sq. cm. tor trans¬ 
formers immersed in oil or cooled by artificial ventilation. I he iollowing 
equations and values have been derived from the foregoing premises; 

B>'2=7.806X10“X(^ L ) 5 (Y) 8 X^-X £ ^r a >- 


a _£f xJLxJ^ 


(2V 


10 8 P 


Total heat dissipated, Hi =2 X 18S 1 - 6 10“ n , in watts per sec. (4). 

Z 71 


w 

2 7T 

= frequency; 

£7 = total exposed 

surface X — 

Vx 

Sa 

Vx ’ 

b 

zi = -; x 

11 

X 

= 4 i =0.25 

A 

0.5 

1 

1.5 

2 

2.5 

3.5 

3*1 

=—-6 
a 

3 

2 

1.66 

1.5 

1.4 

1.285 

X 2 

-A-1.5 

n\ 

2 

3 

4 

5 

6 

8 

0 

= — =6.83 

4.76 

3.46 

2.83 

2.46 

2.22 

1.92 


(Read thus When x = l, xi=2, x 2 = 3, and £1=3.46, etc.) 

w 

Example Core transformer; P = 10,000 watts, E = 3,000 volts, — = 100, 

x — 1, and from previous tables xi = 2, ^ = 3, —n = 1.086, and g = 3.46. 

Substituting in (1), (2), (3), and (4), P = 2,747 lines per sq. cm., n x (primary) 
-=853 turns, a = 10.1 cm., 6 = 20.2 cm., ai=8.25 cm., 6, =24.75 cm., A =^A X 












TRANSFORMERS. 


153 


-204.2 sq cm., v=17,G00 cu. cm., 7; 1 = 19,110 cu. cm., v + n =36,7 JO ou. 
nnVi ‘.iiu os Efficiency = watts output-5-watts supplied = 

(10,000 218.3) : 10,000—97.82%. If the iron section is taken a» one- 

half that of the coils, * = 0.5, ^=0.796, ajj-3, — = 2, g = 4*6, v = 15,940 

off -Q 7 ’A^ 12,700 o U ‘- cn > * + ®t“ 28,640 cu. cm. 1 , /A =222.6 watts, and 
elt.-97.74%, or a dissipation of but 4 watts more than in the first case, 
and a reduction in weight of one-third. 

For shell transformers, £ 9 . 2 = 7 . 866 X10 55 (—) 5 (—)*(—) ? (5) 


X— X— 

(o s v i 36£'-6 


(6), and m = 10 8 £—* 2 #^ai 2 (7). 


_6i .Sai T 

Xz a x ' Q v\’ ^ 1S case ’ w here (e.g.) x = l, and the iron parts cor¬ 

respond to the copper parts in a core transformer, the values of — in the 

b ° l 

table are used for — and similarly those of — in table for —. 

CL CL CL-y 

Taking the data of the example given, it will be seen that in this cas 9 

b\ 

— =2 instead of 3 as for a core transformer. Substituting the various 

values in (5), (6), and (7), the following values are obtained- £ = 2,896 
n\ =813, o=8.22, 6 = 24.65, «i = 10.07 bi =20.13, A —Ai =202.7. v = 18,89o! 
v i = 17,400, w + V! =36,290, H x =216 2; eff. =97.84%, or substantially the 
same total volume and efficiency as for the core transformer first con¬ 
sidered. If the iron section be made equal to twice the copper section. 
£ = 3.091, v = 13,060, V\ — 16,400, v + i>i = 28,140 cu. cm., H x =226.6, eff. 
= 97.73%. If iron section = copper sectionX5, £ = 3,770, v = 7,632, 
V\ ~ 13,640, v + vi = 21.000, Ht = 260.2; eff. =97.4%. 

When a transformer is in circuit continuously, but loaded for only a 
few hours in the day a greater all-day average efficiency is obtained by 
designing the transformer so that the iron heat dissipation is considerably 
less than that of the coil at full load; the efficiency, however, is smaller, 
on full load. In this case the right-hand members of (1) and (5) must 

be multiplied by , and those of (2) and (6) by—, where m = total heat 

W 171 

dissipation -4- hysteresis dissipation. 

If m = 3 (other data as for shell transformer where £ = 2.896), then, 
£ = 2,195, v = 21,180. v x = 19,510, w + t* =40,690, //iron =77.9 watts, // coppcr = 
155.8 watts, H x =77.9 +155.8=233.7 watts. Eff. =97.66%. The weight 
is thus increased about 12% and the efficiency lowered by 0.18%. If the 
load, however, is on only about 6 hours out of the 24, there is a saving 
of about 600 watt-hours per day. 

It is assumed in the foregoing w-ork that the coil and core sections are 
rectangular. If the iron laminations are rectangular and the wires in 
the coils are bent in the arc of a circle w-hen rounding the corners of the 
iron core (which is the most general construction), then, for a core trans- 


6i 


4+(|-l)a 


former, 

ai b — a 

All-Day Efficiency, 
then 


5 + .57a , n / , 

-; 1 = 2 (a i+ 

» — a \ 


7ta 
"ai ~4 


h — 2^a+~+2ai^ 


Let y = No. of hours per day when full load is on; 


All-day efficiency = 


Full load X y 


Core lossX24 + copper loss Xy + full loadX y 


Magnetic Densities in Various American Transformers: 

For 25 cycles, 

£=9,000 to 10,000 lines per sq. cm. (60,000-90,000 per sq. in.). 
For 60 cycles, 

£ = 6,000 to 9,000 lines per sq. cm. (40,000-60,000 per sq. in.) 







154 


ELECTftOTECftNlCS 


Insulation between lampions Ts about 10% of total assembled th.ek. 

, ess; vol. iXr°' 9 The U & C e?Smy of first cost may be obtained 
Economic Design. I he ^‘ S J; e f ^ auac j ty but with various 
I >y calculating several transform^ results and balancing the annual 

atios of copper toiron, g sa v e d (i a bor cost being substantially a 

I r* «« the extra watt-hours per year 

^crificed by cheapening the construction. 


CONDUCTORS. 


Copper-Wire Table, A. I. E. E. 20 C. 


Cauge. 
i>. & S. 

Diameter. 

Inches. 

Area. 

Circular mils. 

Weight. 
Pounds per ft. 

Length. 

Feet per lb. 

0.460 
.4096 
. .3648 
.3249 
.2893 
. 2576 
.2294 
.2043 

1819 
. 1620 
. 1443 
. 1285 
. 1144 
. 1019 
.09074 
.08081 
.07196 
.06408 
.05707 
.05082 
.04526 
.04030 
.03589 
.03196 
.02846 
.02535 
.02257 
.02010 
.01790 
.01594 
.0142 
.01264 
.01126 
.01003 
.008928 
.00795 
.00708 
.006305 
.005615 
.005 
.004453 
.003965 
.003531 
.003145 

211,600 

167,800 

133,100 

105,500 

83,690 

66,370 

52,630 

41,740 

33,100 

26,250 

20,820 

16,510 

13,090 

10,380 

8.2.34 

6,530 

5,178 

4,107 

3,257 

2,583 

2,048 

1,624 

1,288 

1,022 

810. 1 
642. 4 
509.5 

404 

320.4 
254. 1 

201.5 
159.8 
126.7 

100.5 
79.7 
63.21 
50. 13 
39.75 
31.52 
25 

19.83 
15.72 
12.47 
9.888 

0.6405 
.5080 
.4028 
.3195 
.2533 . 

.2009 
. 1593 
. 1264 
. 1002 
.07946 
.06302 
.04998 
.03963 
.03143 
.02493 
.01977 
.01568 
.01243 
. 009858.—£ 
.007818 
.006200 
.004917 
.003899 
.003092 
.002452 
.001945 
.001542 
.001223 
.0009699 
.0007692 
.0006100 
.0004837 
.0003836 
.0003042 
.0002413 • 
.0001913 
.0001517 
.0001203 
.00009543 
.00007568 
00006001 
.00004759 
.00003774 
00002993 

1.561 

1.969 

2.482 

3.13 

3.947 

4.977 

6.276 

7.914 

9.*98 

12.58 

15.87 

20.01 

25.23 

31.82 

40. 12 

50.59 

63.79 

80.44 

101.4 

127.9 

161.3 

203.4 

256.5 

323. 4 

407.8 

514.2 

648.4 

817.6 

1,031 

1,300 

1,639 

2,067 

2,607 

2,287 

4,145 

5,227 

6,591 

8,311 

10,480 

13,210 

16,660 

21,010 

26,500 

33,410 

0000 

000 

00 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 






























CONDUCTORS 


155 


Copper-Wire Table— {Continued). 


Gauge. 
B. &S. 

Weight. 

Pounds per ohm. 

Length. 
Feet per ohi 

0000 

13,090 

20,440 

000 

8,232 

16,210 

00 

5,177 

12,850 

0 

3,256 

10,190 

1 

2,048 

8,083 

2 

1,288 

6,410 

3 

810 

5,084 

4 

509.4 

4,031 

5 

320.4 

3,197 

6 

201.5 

2,535 

7 

126.7 

2,011 

8 

79.69 

1,595 

9 

50.12 

1,265 

10 

31.52 

1,003 

11 

19.82 

795.3 

12 

12.47 

630.7 

13 

7.84 

500. 1 

14 

4.931 

396.6 

15 

3.101 

314.5 

16 

1.950 

249.4 

17 

1.226 

197.8 

18 

.7713 

156.9 

19 

.4851 

124.4 

20 

.3051 

98.66 

21 

.1919 

78.24 

22 

.1207 

62.05 

23 

.07589 

49.21 

24 

.04773 

39.02 

25 

.03002 

30.95 

26 

.01888 

24.54 

27 

.01187 

19.46 

28 

.007466 

15.43 

29 

.004696 

12.24 

30 

.002953 

9.707 

31 

.001857 

7.698 

32 

.001168 

6 . 105 

33 

.0007346 

4.841 

34 

.0004620 

3.839 

35 

.0002905 

3.045 

36 

.0001827 

2.414 

37 

0001149 

1.915 

38 

00007210 

1.519 

39 

.00004545 

1.204 

40 

.00002858 

0.955 


Resistance. 


Ohms per 
pound. 


0.00007639 
.0001215 
.0001931 
.0003071 
.0004883 
.0007765 
.001235 
.001963 
.003122 
.004963 
.007892 
.0-1255 
.01995 
.03173 
.05045 
.08022 
.1276 
.2028 
.3225 
.5128 
.8153 
1.296 
2.061 
3.278 
5.212 
8.287 


13.18 

.02032 

20.95 

.02563 

33.32 

.03231 

52.97 

.04075 

84.23 

.05138 

133.9 

.06479 

213 

.0817 

« 338.6 

.103 

538.4 

.1299 

856.2 

.1638 

1,361 

.2066 

2,165 

.2605 

3,441 

.3284 

5,473 

.4142 

8,702 

. 5222 

13,870 

. 6585 

22,000 

. 8304 

34,980 

1.047 


Ohms per 
foot 


0.00004S93 
.00006170 
.00007780 
.00009811 
.0001237 
.0001560 
.0001967 
.0002480 
.0003128 
.0003944 
.0004973 
.0006271 
.0007908 
.0009972 
.001257 
.001586 
.001999 
.002521 
.003179 
.004009 
.005055 
.006374 
.008038 
.01014 
.01278 
.01612 


The table is calculated for a temperature of 20° C. Resistance in inter¬ 
national ohms. For resistance at 0° C., multiply values in table by 0.9262; 
for resistance at 50° C., multiply by 1.11723, and for resistance at 80° C.,’ 
multiply by 1.23815. The following data were used in computing the 
table: Specific gravity of copper = 8.89. Matthiessen’s standard 1 meter- 
gram of hard drawn copper at 0° C. = 0.1469 British Association unit 
(B.A.U.) = 0.14493 international ohm (1 B.A.U. = 0.9866 international 
ohm.) Ratio of resistivity of hard to soft copper = 1.0226. Temperature 
coefficients of resistance for 20°, 50°. and 80° C. (cool, warm, and hot) 
taken as 1.07968, 1.20625, and 1.33681, respectively. 

Aluminum Wires at 75° F. (Pittsburgh Reduction Co.). 

































1SG 


ELECTROTECHNICS. 


Feet per ohm. 

12,229.8 

9,699 

7,692 

6.245.4 

4.637.4 
3,836.2 
3,036.1 
2,412.6 


Gauge. Ohms per 
B. & S. 1,000 ft. 

0000 0.08177 

000 .1031 

00 •1300 

0 .1639 

1 .2067 

2 .2608 

3 .3287 

4 .4145 

Conductivity taken as 60% of that of pure copper 
aluminum taken as 167.111 lbs. per cu. ft. 

General Formulas for Wiring. ( E y^ ^Intine^ 

Area of conductor m circular rmls = Z>R Weight of copper 

PEM — 100" Current in mam conductors = WTE , Weight oi coPP^ 1 
in line = A WKD 2 + PE X 10°; where D = distance of transmission (one way) 
in feet W = total watts delivered at the end of line, P —per cent loss o _ 
in line’ and E = voltage between the conductors at. the receiving e d 
line A K, and T are constants having the followmig values. 


Ohms per lb. 

0.00042714 
.00067022 
.00108116 
.0016739 
.0027272 
.0043441 
.0069057 
.0109773 

Weight of pure 


Single-phase. 6.04 

Two-phase (4 wires) . . 12.08 
Three-phase (3 wires). 9.06 


100 

2160 

1080 

1080 


100 


-Per cent power, factor 

95 1 

90 

85 

2400 

2660 

3000 

1200 

1330 

1500 

1200 

1330 

T 

1500 


80 

3380 

1690 

1690 


Single-phase.. ^ 

Two-phase (4 wires).6 0 

^ofcontSuo^c'urrent^ieO. j-M-W, and U-U 

-Wires 18 in. apart from c. to c 


—Per cent power 
95 90 

factor 

85 

80 

1.05 

1.11 

1.17 

1.25 

.53 

.55 

.59 

.62 

.61 

.64 

.68 

.72 

= 6.04, 

and M — 

1 . 



Gauge: 
B. & S 

0000 

000 

00 

0 

1 

2 

3 

4 

5 

6 

7 

8 


Values of M. 

25 Cycles. 

-Power factor in per cent. 


40 Cycles. 

Power factor in per cent. 


95 

90 

85 

1.23 

1.29 

1.33 

1.18 

1.22 

1.24 

1.14 

1.16 

1.16 

1.10 

1.11 

1.10 

1.07 

1.07 

1.05 

1.05 

1.04 

1.02 

1.03 

1.02 

1.00 

1.02 

1.00 

1.00 


80 

1.34 

1.24 

1.16 

1.09 

1.03 

1.00 


95 

90 

85 

80 

1.52 

1.53 

1.61 

1.67 

1.40 

1.41 

1.48 

1.51 

1.25 

1.32 

1.35 

1.37 

1.19 

1. 24 

1.26 

1.26 

1.14 

1.17 

1.18 

1.17 

1.11 

1.12 

1.12 

1.10 

1.07 

1.08 

1.07 

1.05 

1.05 

1.06 

1.03 

1.00 

1.03 

1.01 

1.00 


1.02 

1.00 




60 Cycles. 

-Power factor in per cent 


1.01 

1.00 


95 90 85 80 

0000 1.62 1.84 1.99 2.09 

000 1.49 1.66 1.77 1.95 

00 1 34 1.52 1.60 1.66 

0 1 31 1.40 1.46 1.49 

1 1 24 1.30 1.34 1.36 

2 1 18 1.23 1.25 1.26 

3 1.14 1.17 1.18 1.17 

4 1 11 1.12 1.11 1.10 

5 1.08 1.08 1.06 1.04 

6 1.05 1.04 1.02 1.00 

7 1.03 1.02 1.00 

8 -1.02 1.00 

9 1.00 

10 . 

The values of M in the above table 


125 Cycles. 

-Power factor in per cent.- 


95 

90 

85 

80 

2.35 

2.86 

3.24 

3.49 

2.08 

2.48 

2.77 

2.94 

1.86 

2.18 

2.40 

2.57 

1.71 

1.96 

2.13 

2.25 

1.56 

1.75 

1.88 

1.97 

1.45 

1.60 

1.70 

1.77 

1.35 

1.46 

1.53 

1.57 

1.27 

1.35 

1.40 

1.43 

1.21 

1.27 

1.30 

1.31 

1.16 

1.20 

1.21 

1.21 

1.12 

1.14 

1.14 

1.13 

1.09 

1.10 

1.09 

1.07 

1.06 

1.06 

1.04 

1.02 

1.04 

1.03 

1.00 

1.00 

-e about true for 

10% line loss. 










CONDUCTORS. 


157 


a T ml V .r„? f . r eSSh h 'for“a?i a r‘ e io f ?i s IOSS f? fe 3 , tha " , 10 %’ ™der 40 cycles 
at 125 cycles and the losses greater than^O^Ti^ co . nductors are used 
used. If the conductors are If L r, 2 ®7 °’ the val,les should not be 

will be less than that ^ven by the formula andV^ 18 , inches - ‘he loss 
in a cable, the loss will be that due to ret, si ^ d ° Se to «ether, as 

Tor a direct-current 3-wire system tU nf n ? e f on , ly - 
section equal to one-third of thafo?the outshS^l- eeder s, l° uId have a 
F ° r both alternating and direct a " ° bt ? ined trom 

t 8 he\ t SLi^on& ShOU;d h “ Ve the MS y JSriS 

circSTt calculate the primary 

size of the power wire to be to f °'? r ^6 outside wires, the 

amperes) is \o the Sal toad 1^ amwres SecenT 6 - * h ?. m <*°* load (in 
motors should all be of the same size as w? r ° d - an< ? s leadin g to induction 
same capacity in kilowatts mid same nowJr r L ircuit of the 

a be c ° f eqUal ^ss-secttn 6 tW Unes of 

Lighting only, 95%; hlSgTnd abIe ’ f f kc as follows ’ 

lighting circuits using small transformers the’ ni< ?t° rs only, 80%. For 
primaries should be 3% higher than th^vnluJl v vol . ta S e , at transformer 
For motor circuits substitute 5% for 8 °7 in a f eXratl ° of transformation. 
Examples .—Direct-current Srcuft f °000 110 ^ mg rule ’ u , 

O.o ampere; line loss 10 °7 • ^r* 9 i• H0-\olt lamps, each taking 

Circular mils -2,160 X 2 000 yKK + «?*• 2.000 feel. B 

Volts drop to lkmpJ-roxniofl^lM^VvoTtl^'OX HO*)-1,963,636. 

Volts loss in circuit = 10 X 220 X 1 — 100 = 22 vnlt« U ' 3 ~ 103,633 cir. mils. 

2 voRft secondary 1 1( U° f transformers 

line to be 5% of the delivered noter S dr ° P= c 3%: lo , ss in Primary 
Vohs at transformer primaries = (110 + 2)X10XI (W = 1 lfi| f « rmer = 9?% ’ 

Watts required by lamps = 1,000X 110 X0 5 — 5 ^ non w' b ‘, 
at primaries = 55,000 = (0 98 X 0 97 ) - 58 non ^'n 7 55, Watts required 
2,400 = (5 X 1,153.62) = 41,760. ; 5 ’° 00 ' Cir * mds = 2 ’ 000 x 58,000 X 

los?, h To e % h of dflhi r 4d P ToweV an rif Si ° n ’ 60 Cycles; 3 ' 500 H.P.. 5 miles; 
of load = 85%. Circular mils - fUjwfv ^w^SS? 0 ’ P°wer factor 
(10X5,0002) = 413,582. Two 0000"w mfha 1 (3 ’ 500 ^ 74 r 6) X *.500 + 

f the latter are used the drop will be orfTSlS* ofThaf^us^X 

arger wires (—) . Per cent loss = 5,280X5X3,500X746X1500- 

S X «W-SSL^- 9 v® la,t‘ h fn d H 1 M-B i 7QvTnnn 0 v , 3226 H.P. loss 
Volts at generator = 5,000 + 715 = 5 715 ( , - /9Xo .'°t)0 x L46-f- 100 = 715. 
0.68 = 5,000 = 355 amperes ’ Current in line = 3,500 X 746X 

— Line Constants. (Wires 18 in. apart.) 


-unit? 

Cauge, Wt„ Diam. Area, 
-t>. & S. lbs. mils. cir. mils 
0000 3,376 460 211,600 
000 2,677 410 
00 2,123 365 
0 1,685 325 

1 1,335 289 

2 1,059 258 

3 840 229 

4 666 204 

5 528 182 

6 419 162 

7 332 144 

8 263 128 


C. 

.0102 
.00996 


167,800 

133.100 
105,500 

83,690 

52,630 1.067 1.70 .00883 
41,740 1.346 1.73 - 

33.100 1.700 1.77 

26,250 2.138 1.81 00827 


t. 

.0385 


/ = 


R. L. 

.266 1.48 
.335 1.52 
•422 1.56 
.533 1.60 

• 671 1.63 ^ 

.845 1.66 .00909 .0342 .261 


Reactance, X,- 

=25 40 60 125. 


n5 -- 232 372 • 5 58 1.16 
.0375 .239 .382 .573 1.19 


-- • v ww . x , “rvyw 

.00926 .0349 .256 .409 


.00973 .0366 .245 .392 588 1 22 
00949 .0358 .251 .402 .603 1 26 

.614 1.28 
•625 1.30 
.641 1.33 
.652 1.36 
.667 1.39 
.682 1.42 
693 1.44 


.417 

.427 


- .0333 .267 

.00863 .0326 .272 435 

00845 .0319 .278 445 

nnoney Q312 934 .455 


20,820 2:698 l'.84 !00809 0305 289 462 693 1 

16,010 3.406 1.88 . 00793 . 0295 .'!! A72 irof 



158 


ELECTROTECHNICS. 


Weight given in lbs per mile of trite; 

L = inductance in millihenrys per , ™de, I cu Vrent of line of two 

We." 1 ') = 6U a ° V-IO'OOO ‘votof-^/CBlO-t; X = reactance-2*//. 10-. 
Im ff, d ft n S’ required 2 to^rausmit ^00 over a 3 , circuit 10 mUes 

in length the powe,i b^X'fo^raMmiSon^ tag the line, and reduced 
up transformer to 10.000 \ 0l . ts 10 ” r r" 11 l D . down transformer. Trans- 
to 1,000 volts at the receiving end by a .® h iV- core or hysteresis 
former efficiencies— 97.5%; coppei s maeneti'zing current = 4%. Loss 

in pach 1.5%; reactance = 3.5%, magnetizing cuiiciib /« 

inTr'ansmkision = 15%, 10 of which is in line; power factor - (L85. \ oltage 

between any branch and the common center of system^ -i^ 3 _ 

10,000 = ^3 = 5,774. Energy delivered b ^. £ 7 \ 400 “= 0°85 = 790,000 

671,400 watts. /^PParent energy per branch f, 8 amperes . Drop in 
watts. . Current m ea« h wire-790 000 -5,774^3 ^ 57? 

* h x:r^Ls 

°„? 1 w hS 

?„ 0 r rn U Sres° X o l66X 10 = 0.W66 amp y Power factor being 0.85, the induct- 

MMBfe 

convenience in calculation___..____ 

Impressed E.M.F. = 2 (energy E.M.F.’s) 2 -!-^ (Induction E.M.h.’s,- 

Commencing with the secondary circuit, working back and tabulating the 
steps, the following is obtained: 


Secondary Circuit: 

Energy, E.M.F. — 5.774X0.8.) 
Inductive E.M.F. = 5,774X0.52 
Current, in amperes 
Step-down Transformers: 

Resistance loss, 772 — 1% °f ^,774 
Reactance “ 7X = 3.5% of 5,774 
Hysteresis “ —1.5% of 136.8 


distance loss, 1R = 138.85 X 4 1.22 
Reactance IX— 138.80 X5.88 

(Volts at terminals of step- up trans¬ 
formers = V5,553 2 + 4,0222 = 6,857.) 
Step-up Transformers: 

Resistance loss, IR — 1 % Ot857 

Reactance “ 7X = 3.5% of 6,8o7 
Hysteresis 41 1.5% of 138.80 


Energy 

E.M.F. 

= 4,909 


= 58 


4,967 
= 586 


5,553 


= 69 


5,622 


Inductive 

E.M.F. 


3,003 


202 


3,205 


817 

4,022 


240 


4.262 


Current. 


136.8 


2.05 
138.85 


138.85 


2.08 

140.93 


,„Y?ati a o! rf|Mj 

° f Inductance'for pirallS Copper Wires, Insulated. L per 1,000 feet 
per wire = 0.01524+ 0.14 log L per 1,000 ft. of the whole circuit for a 


















CONDUCTORS. 


159 


3-phase line-0.02639 + 0.2425 log i where /. is in millihenry*. d and r 

IffSStif'.lftJr ° enterS ot wires “<< »<«>» of «'ine, 

Capacities of Conductors. lead-protected cables: Microfarads per 
1.000 ft. of length =0.00736177-r log Single overhead conductors, with 

earth return: Microfarads per 1,000 ft. =0.007.361 - 5 - log —. 

Each of two parallel, bare aerial wires: Microfarads per 1,000 ft. =. 
0.003681 + log -A In the above, D = diam. of cable outside of insulation, 

unh! ing raatena1 ’ D% d ' du h ’ and r shoulcl all be measured by 1 the°same 

Heating of Conductors. Insulated parallel wires: Diam in inches- 
0.0147^/ 2 f Kennedy). Bare wires; Diam. in mils 
S d«» F CUrre “ amiJeres - of "ire. and (-temp, if air, boft 

Carrying Capacity of Interior Wires and Cables (A. I. E E ) 

B. & S. Rubber- Weather- Circular Rubber- Weather- 

mils. covered, proof. 
400,000 330 500 

600,000 450 680 

800,000 550 840 

1,000,000 650 1000 

1,500,000 850 1360 

2,000,000 1050 1670 

The capacities are in am¬ 
peres. No smaller wire 
than No. 14 to be used. 

Rubber covering to be A in. thick for No. 14 to No. 8, * in. for No 7 
.No. 2, m. for No. I to 0000, ^ in. for No. 0000 to 500 non cir m ;i, 
bV in. up to 1,000,000 cir. mils, and i in. above 1,000,000 cir. mils Weather- 

EJetroS^ coating 

Insulation Resistance (National Code). The wiring in complete instal ¬ 
lations must have an insulation resistance - ( -— ,Q00 ’ 000 A ; n nt , rio 

p f _ , , Vamperes flowing/ in °hrns. 

• u Se ?*. Fus f s , f ?^ 5 al «Peres and less should be 1.5 in long and 0 5 
in. should be added for each additional 5 amperes. Round w re fhouhl not 
be used for over 30 amp.-above that, use a flat strip. FusingcSrent- 

ZZi'J 1 '.* d ~i a £ n aj 1 J 1 in , che ® and n 1S a eonstant having the following 

2 a &+Tti„;Mi 8 . plati ' lum ' 5a72; 

Diameter in Inches. 


Gauge. 

covered. 

proof. 

14 

12 

16 

12 

17 

23 

10 

24 

32 

8 

33 

46 

6 

46 

65 

4 

65 

92 

2 

90 

131 

0 

127 

185 

000 

177 

262 

0000 

210 

312 


Amperes. 

Copper. 

Iron. 

Tin. 

Lead. 

1 

.0021 

.0047 

.0072 

.0081 

10 

.0098 

.0216 

. 0334 

0375 

50 

.0288 

. 0632 

. 0975 

1095 

100 

.0457 

. 1003 

.1548 

1739 

200 

. 0725 

.1592 

. 2457 

.276 

300 

.095 

. 2086 

.322 

.3617 (Preece.) 


ELECTRIC LIGHTING. 

Arc Lamps. 45 to 60 volts, 9.6 to 10 amp., 2,000 candle-nowpr 
nal); 45 to 50 volts, 6.8 amp., 1,200 candle- power ( nominal). Enclosed 
arcs require 80 volts, 5 amperes; carbons burn from 100 to 150 hours 
Alternating-current arc lamps require 28 to 30 volts and 15 amperes. 







160 


ELECTROTECHNICS. 


The mean spherical candle-power (c.-p.) is the mean of that fjver^a 

sphere of which the light is the center and equals, approximately, ^ 4 ’ 

where H is the horizontal c.-p. and M the maximum c.-p. (40° below hori¬ 
zontal for a direct-current arc). The continental unit of light is the hetneii 

or 0.88 candle-power. , , , . „ 

Clear-glass globes cut off 10% of the illumination, ground-glass globes 
from 35 to 50%, and opal globes from 50 to 60%. _ 

Incandescent Lamps, usually 16 c.-p., require from 3 to 3.5 watts 
per c -p and have a life of 800 to 1,000 hours. They should not, however, 
be used over 600 hours, as their efficiencies decrease during use. 1 he 
most economical point at which to renew a lamp (i.e. the smashing 

point) may be found as follows: _ 

Hours lamp should be used = B E, where B== cost of lamp per c.-p., 
E — cost of 1,000 watt-hours of energy, and c = 1,410 when the increase 
of watts per c.-p. per hour of use =0.001 (c = 1,000 wdien increase = 0.002, 

and 815 when increase =0.003). . . ,, , 

The Tantalum Incandescent Lamp has a fine w ire of this rare metal 
in place of the ordinary carbon filament. Properties of tantalum: melting 
point = 2,300° C., sp. heat =0.0365; sp.g. =16.5; sp. resistance (lm.Xlmm. ) 
= 0.165 ohm. The resistivity increases wdth the temperature and at 
1.5 watts per c.-p. =0.855. Lamps (1.5 watts per c.-p.) nave a usetu 

life of 400 to 600 hours. A , ... . .. 1nn 

Illumination. Arc lamps: for outdoor or street illumination, 1UU to 
150 sq. ft. per w'att; for railway stations, 10 to 18 sq. ft. per watt; for 
large halls, exhibitions, etc, 2 sq. ft. per watt; for reading-rooms, 1 sq. ft. 
per watt and for intense illumination 0.5 sq. ft. per watt. 

Incandescent lamps: (16 c.-p.). Ordinary illumination, sheds, depots, 
etc. 1 lamp (8 ft. from floor) for 100 sq. ft.; waiting-rooms 1 lamp for 
75 sq. ft.; stores and offices, 1 lamp for 60 sq. ft. Dark walls require an 
increase in the above figures. Nernst lamps, having a glower formed 
of metallic oxides which becomes incandescent during the passage of current, 
are made in sizes from 25 to 150 c.-p. and require about 1.6 watts per c.-p. 


ELECTRIC TRACTION. 


Tractive Force and Power. The force, F, required to bring a car 
from rest to a certain speed, s, (in miles^ per hour,) within a given time, 

t, (in seconds,) is F (in lbs.) = / + + 20TI>, where IT=weight of 


car in tons, / = (20 to 30)XTT, and p = per cent of grade. 

It takes a pull of about 70 lbs. per ton to start a car on a level or to 
round a curve. If there is a grade, the starting pull in lbs. = (70 + 20p) \V , 
ba^ed on a speed of 9 miles per hour being attained in 20 secs. 

The average II.P. required = 0.00133-Fs-i-r,, where 19 = efficiency of motor 
(from 50 to 60%). The per cent grade, p, at which slipping occurs when 


car is starting =- 3.5, wdiere a = ratio of adhesive force to weight on 

jC 

drivers =0.125 to 0.16. and x = weight on drivers = total weight of car. 

100a _ 

When running, p = — -1-5. 

Resistance of Rails used for Returns. Cir. mils of cross-section of a 
rail = 124,750 W; equivalent cir. mils of rail section in copper = 20,800 W ; 
Resistance of a single rail per mile in ohms = 2.5IF, approx. (Varies 
from 2.5 to 5 according to the chemical composition of rail.) \V = weight 

of rail in lbs. per yard._. 

Safe Current for Feeders, in amperes, = V(diam. in mils) 3 - 4 - 1,300. 
Heavy Electric Railroading. Train resistance, R, in lbs. per ton 

of 2,000 lbs. = 3+ 1.67s + 0.0025-^-, where s = speed in miles per hour, 

A = cross-section of car in sq. ft., w = weight of train in tons of 2,000 lbs. 
This formula ivas found aoolicable to conditions met with on the Long 
Island Ry. (W. N. Smith/A. I. E, E., 11-25, 1904). 








ELECTRIC TRACTION. 


161 


A formula due to Aspinall is said to give satisfactory results: 
?JV 1 lbs. per metric ton of 2,200 lbs. ) = 2.5+ s3-h (51+0.028L), where 
/>-length ot train m feet- I he starting resistance varies according to 
the wheel diameter, condition of track, etc. Aspinall gives as a fair average 
17 lbs. per ton of 2.200 lbs. for best conditions. 

Electric Passenger Locomotive (N.Y.C. & H.R.Ry.). Type 2-8-2: 
dmers 44 in. diam.; trucks, 36 in. diam.; diam. of driving axles = 8.5 in • 

vjcnoom uf dnvers = , 15 ft., total wheel-base = 27 ft. Weight, on drivers = 
138,000 lbs.; on trucks, 52,000 lbs.; total weight = 190,000 lbs 

lower: direct current, 600 volts; 4 motors, each 550 rated II I*. Max¬ 
imum power = 3,000 H.P. Normal full-load current = 3,050 amperes 

, am !>- Normal draw-bar pull = 20,400 lbs., max 
P,, 3-,000 lbs. Speed with a 500-ton train = 60 miles per hour. (General 
Electric Co., builders.; 


ADDENDA. 


Large Gas Engines. Belgian and German Practice. Compression, 
I/ 0 ,. 10 200 lbs. per sq. in.; m.e.p. generally taken as 70 lbs. per sq. in 
Cooling-water per B.H.P. per hour: cylinders, cylinder-ends and stuffing- 
boxes, 4 to 5.25 gal.; pistons and piston-rods (hollow), 1.75 to 2.75 gal.- 
\ £il\e-boxes, sests and exhaust-valves, 0.88 to 1.38 &al. (Water entering 
at 60° F. and leaving at 95° to 115° F.) Engines are started by com¬ 
pressed air (150 to 250 lbs. per sq. in.) and the lubrication is effected by 
means of a forced oil-feed. The foregoing for engines of 200 to 1,000 H.P. 

An Otto-Deutz 4-cycle, double-acting engine (223 B.H.P.) using suction- 
producer gas made from Belgian anthracite (14,650 B.T.U. per lb.) re¬ 
quired 0.704 lb. of dry coal per B.H.P. hour. (R. E. Mat hot, Liege Meet¬ 
ing of I. M. E., 1905.) 

Shearing Strength of Rivets in lbs. per sq. in. Single-shear: Iron 
40,000; steel, 49,000. Double-shear: Iron, 78,000; steel, 84,000. Dis¬ 
tance from center of rivet hole to edge of plate should be about 2d. (E. 

S. Fitzsimmons, Master Steam-Boiler Makers’ Convention, 1905.) 

A safety factor of 44 should be employed. In butt-joints with two 
butt-straps or cover plates the rivets are injiouble shear (page 21). 

Flow of Air in Metal Pipes. Q = cV~- , where d = side or diam. in 

1j 

in., F — friction in ounces per sq. in., L = length in ft., Q = cu. ft. per 
min., c = 4.4 for round and 5.5 for square pipes. For a 90° bend in the 
pipe, add E feet to L. (E = kd .) Let r = mean radius of bend in in. 

Then, when r-z-d = 0.5 1 1.5 2 

k =5 43 2 

(J. H. Kinealy, E. N., Aug. 10, 1905.) 
When r = 2.5 d the bend offers the least resistance, and E (in inches) = 
3.38 X lengt h of the curved portion of pipe, measured along the center line 
at radius r. (C. W. L. Alexander, Trans. I. C. E., 1905.) 






APPENDIX. 


MATHEMATICS 


Metric II.P. (Force de cheval). 1 metric H.P. = 75 m.-kgs. per sec.= 
542.475 ft.-lbs. per sec. = 0.9863 British H.P. (I British H.P. = 1.01389 
metric HP.). 1 meter-kilogram (m.-kg.) =7.233 ft.-lbs. 1 ft.-lb — 

0.138255 m.-kg. 

Guldinu.s’ Theorems for Areas ami Volumes. _ , 

1. if a straight or curved line in a plane revolves about an axis lying in 
that plane, the area of the surface so generated is equal to the length of 
the line multiplied by the distance through which its center of gravity 


2. If a plane area revolves about an external axis in the same plane, 
the volume of the solid so generated is equal to the area of the figure mul¬ 
tiplied by the distance through which its center of gravity moves. 

Centers of Gravity of Lines. Straight line: Its middle point. 
Circumference of a triangle: Form an inner triangle by connecting middle 
points of sides and inscribe a circle; the center of circle is c. of g. desired. 
Circumference of parallelogram: At intersection of diagonals. Circular 
arc: On middle radius at distance x from center of circle [.t = (chord X ra¬ 
dius) -h length of arc]. For very flat arcs c. of g. lies f/i from chord, where 
h = height of arc. _ 


MATERIALS. 


Metals, Properties of. 



Sp. G. 

Lbs. per 
cu. in 

Fusing- 

points. 

Antimony. 

. 6.7 

0.242 

806° F, 

Bismuth. 

. 9.8 

. 354 

51 6 

Lead.'. 

. 11.38 

.411 

620 

Manganese. 

. 8. 

.289 

3,452 

Nickel. 

. 9. 

.325 

2,678 

Platinum.. 

. 21.5 

7 76 

3,272 


Allovs. Sterro Metal (Tensile strength T.S. = 60,000 lbs. per sq. 
in )■ 55% Cu + 42.36% Zn + 1.77% Fe + 0.1% Sn + 0.83% P. Wolfram- 
iniums 0.375% Cu + 0.105% Sn + 98.04% Al + 1.442% Sb + 0.038 W. 
Magnalium: 2 to 25% Mg + 98 to 75% Al. Sp. g., 2.4 to 2.54; fusing- 
point 1,100° to 1,300° F. With 10% Mg, alloy has properties of rolled 
zinc- with 25%, those of bronze. Parsons’ Manganese Bronze : 60% 
Cu + 37 5% Zn + 1.5% Fe + 0.75% Sn + 0.01% Mn + 0.01% Pb (for sheets); 
56% Cu + 42.4% Zn + 1.25% Fe + 0.75% Sn + 0.5% Al + 0.12% Mn 
(for sand castings). T.S. = 70,000 lbs. per sq. in.; elastic limit, 30,000 
lbs.; elongation in 6 in. = 18%; reduction of area = 26%. 

Nickel-Vanadium Steel. (Carbon content = 0.2%.) With 2% Ni, 
and 0.7% V, tensile strength = 90,000 lbs. per sq. in; increasing V to 1%, 
TS =120,000. With 12% Ni and 0.7% V, T.S, = 200,000; increasing V 

162 









APPENDIX. 


163 


to 1% T.S. = 220,000. By tempering the 90,000 lb. steel (heating to 1,560° 
ln , w ^ r a * 68 ° F ') its , T S - is raised to 168,000. Elastic 
12% Nt = 6<7 80 ^ ° f T S ‘ EIongatlon for 2 % Ni steels about 22%; for 

4 'jSr! 1 ivf ble IroM ’ Ultimate Strength. Round bars tensile strength = 
-oSSJr % er SQ - ln - J a PP r ox.; elongation = 7% in 8 in.; reduction of area 
~r' i /0 /o- Square and star-shaped sections have about 85% of the strength 
ot circular sections. Compressive strength is from 31,000 to 34,000 lbs per 
sq. in. (Mason and Day.) 

Steel. Each per cent, of the carbon content of a steel is divided into 
100 parts each of which is called a “point”; thus, a 40-point carbon steel 
is one conta. mg 0.4% of carbon. 

Portland Cement Concrete In Compression (safe strength). /, (di¬ 
rect compression) == 4 260-r-(«+ 0 + 4.4), where s and g are the No of parts 
ot sand' and gravel in the mixture to one part of cement (c). For one cubic 

—n^ A r r ete Vr N ° ° f b ^ ls ' of c ? ment - N = n + (c + 8 + g); No. cu. yds. 
3 8 cu^ ft ) 1 VS: N °' CU ' yt S ' gravel or crus hed stone = 0.141 Ng. (1 bbl.= 


STRENGTH OF MATERIALS. 


Elastic Limit. \ield-Point. Permanent Set. The elastic limit 
is tne point at which the strains begin to increase more rapidly than the 
stresses causing them. This increase of strain is initially slight but 
becomes marked later at what is called the “yield-point” (e.g., when 
scale-beam cf a- testing machine suddenly drops). That part of the 
strain which does not disappear when the stress is removed is called the 
permanent s t. _ If none of the strain disappears on removal of the 
stress, the material is said to . be “plastic.” if the greater part remains, 
the material is ductile, ’ and f the materir.1 breaks under very low stress 

and slight stretch, it is said to be “brittle.” 

Transverse Elasticity (see page 18). In formula C = f 8 + da, d s i s the 
strain between two shear planes 1 in. apsrt. 

i o P a St c e ? S lfi ? ate ) = CXlilt, tensile stress, where C = 

1 z U-l to 11.5) tor L 1. 1 .25 for phosphor bronze and vellow brass, 0 9 for 
gun-metal 0.6 for alloy bronzes, 0.75 for W. I., and 0.12 carbon steel, and 
U.o.) ior 0 /0 carbon steel. (E. G. Izod, Engineer , London, 12—29-'05.) 
Aluminum (99% pure). Breaking and safe stresses in lbs. per sq. in.: 


Tension. 


Compression. 


Castings. 

Sheets, bars. 

Wire. 

Allowable Fiber 


Tension, ft = 
Compression, f c = 
Bending, //> = 
Shearing, / 8 = 
Torsion, f tw = 


Breaking. 

Safe. 

Breaking. 

Safe. 

. 14,000-18,000 

3,500-4,500 

16,000 

3,000 

. 25,000-40,000 

6,000-7,000 

20.000 

5.000 

. 30,000 35,000 

(F = l 1,500,000 for 
cast metal 1 

Stresses m Lbs. per Sq. In. (Bach 


W. I. 

Steel. 


C. I. 

Low 

High 

Cast- 


Carbon. 

Carbon. 

ings. 


12,800 12,800 

17,000 

8,500 

4,300 

17,000 

21,300 

12,800 

12,800 

i t 

12,800 

17,000 

12,800 


t t 

10,700 

15,000 

(a) 

10,200 10,200 

13,700 

6,800 

4,300 

13,700 

17,000 

12,000 

5,100 8,500 

12,800 

(b) 

12,000 

17 000 

< l 


(The higher values are for homogeneous metal, not too soft.) 

(а) For rect. sections, 7,300; circular, 8,800; I sections, 6,200. 

(б) For circ. sections, solid and hollow, 4,300; elliptic and hollow' rcct., 













164 


APPENDIX. 


4 300 to 5,300; rect., square, I, channel, angle, and cruciform sections, 

6,000 to 8,000. , . ii 

The values above given are for constant stresses due to a dead load, f. 

For repeated stresses: 

(1) load fluctuating between 0 and +P, take % of tabular values; 

(2) “ “ “ +p “ - p , “ i “ , “ , ;; 

For spring steel (1), fb = 52,000 (unhardened) or 62,000 ('hardened). 

Strength of Cylinders. According to Prof. C. H. Benjamin, if the 
flanges of a C. I. cylinder are unsupported, the initial fracture will be cir¬ 
cumferential, near the flanges, and will be caused by a pressure much 
less than p = 2 ft-i-d. Also, if flanges are sufficiently braced by brackets to 
insure longitudinal fracture, a considerable allowance (say £) must be 
made for bending and other accidental stresses. Hydraulic cylinders 
under pressures above 3,000 lbs. should be made from air-furnace iron or 
steel castings, as water will ooze through ordinary, open-grain C. I. walls 
<4. in. thick. (A. Falkenau, Am. Mach., l-4-’06.) 

The thickness, t, of the walls of a cylinder under internal pressure, p, 
may be found from the following formula, which is a simplification by the 
author of a rather unwieldy one due to C. Bach: t = 0A‘2pd-r- (/ 1 — p ), where 
d = diam. of cylinder and /, = allowable stress in the material employed (to 
be used only when p<0.77/i). , __ 

Falues of /,: C. I. and bronze, 4,300 to 8,500 (and even 10,000 for strong 
iron); phosphor-bronze, 7,100 to 14,200; cast steel, 14,200 to 17,000 (for 
Mannesmann tubes of Martin steel, 18,000 to 43,000); W. I., 12,800 to 
25,600. t and d in in., p and /, in lbs. per sq. in. 

Cotter Joints (W. I. and Machinery Steel). Diam. of rod, d, is en¬ 
larged to D( = 1.33d) in socket. Socket diam. = 2D = 2.66d; thickness of 
key (steel) = 0.25D; mid-depth of key, h = 1.33D = 1 75d. Ends of socket 
and rod should extend f/i to f h beyond key slots ( = 1.25d, average). 

Fly-Wheels, Safe Velocities for. Velocity in ft. per sec.= 

1.63 V syf( -r- w, where s = factor of safety, 1 ? = efficiency of joint used, w = 
wt. of 1 cu. in. of material, and /, = tensile stress of material. 


Hard Cast 

Maple. Iron. 

w = .0283 .261 

ft = 10,500 10,000 

s = 40 10 


Steel. 

.283 

60,000 

20 


In wooden rims s = 20, but as the segments break joints in assembling 
the strength is reduced one-half, making s really equal to 40. Steel rims are 
made up from segments riveted together, and the usual factor 10 is simi¬ 
larly increased to 20. Using above values and considering wheels as 
solid, jj = l. For cast-iron rims, r/ = 0.25 for flange-joints between arms, 
= 0.5 for pad-joints (each arm having a flat enlarged face on its end to 
which rim-sections are bolted), = 0.6 in heavy, thick-rimmed balance-wheels 
with joints reinforced by steel links which are shrunk on. (W. H. Boehm, 
in Insurance Engineering .) 

Riveted Joints. General Formulas. (W. M. Barnard.) 


d _4t( +d . 

ic ''nfs + 2mjs' 'ft ' 4 k tj t ' 

Efficiency of joint = 1 - 4 - [1+/, -4- (nf r + mf/)]. 

In the above n = No. of rivets in single shear in a unit strip equal to the 
max. pitch (where rows have different pitches), and m = No. of rivets simi¬ 
larly in double shear. / and /' are respectively strengths in single and 
double shear. 

f t (iron) varies from 40,000 for single-riveting, punched holes to 50,000 
for double-riveting, drilled holes. f t (steel) = 55.000 (punched holes) to 
60,000 (drilled holes), fs (iron) = 36,000 to 40,000; f 8 (steel) = 45,000 to 
48,000. 

fr (iron) =67,000 (for lap-joint) and 90,000 (for butt-joint); f c (steel) = 
85.000 (lap) and 100,000 (butt). 

Helical Springs of Phosphor-Bronze will withstand the action of 
salt-water. For wire up to £ in. diam. use formulas on pages 23 and 24, 
taking / 8 = 17,825, and C = 6,200,000. (H. R. Gilson, Am. Mach., 7-19-’06.) 





APPENDIX. 


165 


Moment of Inertia. The following graphic method is in extended 
use among designers of structural steel 

Divide area of section A (Fig 38) into 10 or more strips parallel to 
direction of neutral axis desired, and set off lengths representing their 
respective areas on the polar diagram at the left as 01, 12, 23 mn. 
i nese strip areas are to he considered as parallel forces which act at their 
respective centers^of gravity as indicated by the small circles. Set off 
n ni ’iZ kmg OB = it A , and draw 00, 01, 02, ...On. Draw X0||00. 
i)/ > ’i i ' ' • closing diagram witn nL||On. At the intersection of 
nLl and AO, draw JX, which is the neutral axis of the section. Find the 

' 0 



Fig. 38. 


area of the equilibrium polygon, A,, then, Moment of Inertia of Section = 
area AX area A,. (The greater the number of strips, the more accurate 
the results obtained.) 

Darn mated Springs. For nearly flat springs, Deflection J = TF7 3 
4,460n6( 3 (approx.), but for exact results, as true for buffing as for ordi¬ 
nary springs, Deflection = J[1 -c(5c-7J) +3J 2 ]h- 3/ 2 , where ( = length of 
arc of top plate, c = camber, b and t = width and thickness (all in inches) 
n = No. of plates, and IF = load in tons. (H. E. Wimperis, Engineer, Lon¬ 
don, 9-15-’05.) 

Strength of Forged Rings (for hoisting, etc.). Consider the sus¬ 
pended ring to be divided into two equal parts by a vert, plane, 4 of total 
load Wi acting on each half Employ formula for combined tension and 

bending (page 29) • f t = W (- + ^-) „ where W = -^\ a = nd 2 -i-4, r = 0.5(D + d), 

where D = internal diam of ring and d = diam. of iron used, c = 1.6 for W. I. 
or steel, s = nd 3 ^-32. This reduces to: f,d 3 — 2.23TF,d = 16 IF,/), in which 
ft = 5,000 to 6,000 lbs. per sq. in. for safe tensile stress (allowing for sud¬ 
denly applied load and efficiency of weld). IF, in lbs., d and D in in., any 
two of which being assumed, the third may be derived from formula. 

A formula discussed in Engineering (London), 5-29-’95, and arrived at 
through a different method, is: ftd 3 — 1.62TF.d = 1 62PF,D. 

Columns. Euler’s Formulas. Safe load W = cn 2 EI-i-al 2 , where c~ 
0.25 for one fixed and one free end, =1 for both ends free, load guided, =>2 



































166 


APPENDIX. 


for one fixed end and one free end, with load guided, —4 for both ends 
fixed, load guided; s = safety factor = 5 to 6 for W. I. and steel, 8 or more 
for C. I., and 10 for fir. The above formula should not be used where l 
( = length in in.) is less than 25 d for W. I. and steel, or less than 12 d for 
C. I. and wood, where d = diameter or smaller rectangular dimension of 
cross-section in in. . 

For reinforced-concrete columns, c = l, s = 10, and A — {a + b)kj c -r- (a + 1), 
where F c = modulus for concrete, a = concrete cross-section -5- steel cross- 
section, 6 = E atee i + Ec. m , , . 

For shorter bars subjected to thrust, the following formula, due to 
Grashof, should be employed: 

77 = max. load in lbs. = ckal-t- + cl ), 


where a = sectional area of bar in sq. in.; A; = 12,000 for steel ( = 10,000 for 
W. I.); C = 5,000 for steel and 5,600 for W. I.; c = l for bar free at both 
ends (e.g., connecting-rod), = 4 for bar fixed at both ends. For connecting- 
rods take but 75% of the above values for k. 

Collapse of Tubes. (Lap-welded Bessemer steel, 3 t o 10 in. in diam.) 

Collapsing pressure p, in lbs. per sq. in. = 1,000(1 — ^1 — (1,600( 2 -ed 2 ), 
where (f-s-d) <0.023; p= (86,670*-s-d)-1,386, where (* + d)> 0.023. (Ap¬ 
prox., p = 50,210,000(f-5- d) 3 when «-s-d) <0.023.) These formulas apply 
when i>6 d. A safety factor of from 3 to 6 should be introduced, its size 
being according to the risk at stake to life and property. (R. T. Stewart, 
A. S. M. E„ May, ’06.) 


M 



Torsion and Bending (see also page 31). Accordin g to Bach, Equiv¬ 
alent Bending Moment = 0.35Bm + 0.65 v/ R m 2 4- (<xTm) 2 , ‘where a = 1.9 for 
W. I., 1.15 for soft steel, and 1 for hard steel. 

Cranked Shafts. Let abcedf (Fig. 39) be a horizontal cranked shaft. 
The turning force P (having a moment M, due to wt. of fly-wheel at a and 
equal to Pr ) acts at center (e) of crank-pin in the direction indicated. 
Weight of fly-wheel (17) acts vertically downward at a. Neglecting end 
thrust: 


Bearing reaction at center b (upward) 



T7 (g + h -fi k ) 
h + k 


Pk _ 
h + k' 


1 (downward) _P S _—+— 


Bending and Twisting Moments: at b, B m = Wg, T m ^Pr-, at c, B>n = 
W(m + g)—P\m, Tm = Pr; at d, Bm = P^n, Tm = 0; at e, Bth = P 2 k, Tm — Por ; 
nt x (any point on throw) the moments P ex and P 2 'fx are each to be 
resolved into moments in and also perpendicular to the cross-section and 
then combined. The component in the plane of cross-section gives T m and 










APPENDIX. 


167 


the combottfent petp. to cross-section gives Bm. Similarly for any point y. 
1 should also be assumed as acting downward and above values worked 
out tor that direction. 


Gap Frames for Riveters, Punches, Shears, etc. 


The size and character of the work determine the depth of throat / or 
distance Irom point of application ol force w to the nearer or tension flange 
of frame. Assume the main section of frajne (lying in a plane J_ to direc¬ 
tion of force w) to be of an I-, or equivalent box-section, of area a, and 


(due to w) distributed over it. 


having a uniform tensile stress ^ v _ _ UWM1Uttlsu UVC1 lt JL , CLt . 1 _ 

mine position of the neutral axis of section and also its moment of inertia 7. 

Ihe bending moment Bm (due to w ) on the section = wL =w(l +’r) 
where x = distance from neut. axis to outer fibers of the tension flange! 

due to B m = B m x-hI, and total stress in tension flange = 


Tensile 
B m x w 

l a 


stress 


( 1 ). 


Similarly, stress in compression flange due to B m 
from neut. axis to outer fibers of compression flange. 


B m y 
1 ’ 


where y = dist. 


This stress is opposed by the uniformly distributed tensile stress, 

B m y 


and 




the net stress in compression flange = ' 

la'' 

ff (1) and (2) differ from the safe stresses for the material employed 
(C . I., or cast steel) the area and proportions of section must be altered 
until substantial agreement is arrived at. Sections parallel to direction 


of force w are calculated for bending only, there being no direct stress (—) 

on them, but the webs must have sufficient surplus section to resist shear 
Steel Chimneys (self-supporting). 77 = height; D and 7),=outside 
and inside diams.; 7’ = thickness [ = 0.5 (D - £>,)]; Db = diam.of bell-shaped 
base ( 1.5 D to 27)); H'b = height of base (— Db ). All dimensions in feet. 
Wind pressure P (lbs. per sq. ft.) = (velocity in miles per hour) 2 -e 200. 
P is generally taken at 50 lbs., or 25 lbs. actual pressure per sq. ft. of pro- 
jected area (HD). To this is added 5 lbs. to allow for compression on one 
side, making P gro8 8 = 30. Bending moment, B m = 30HD X0.577 = 15DH 2 . 

Section modulus, >S' = ^-( 7 - 4 ~ /J>|4 ) =0.7854 D 2 T. F (per sq. ft.)=P m = £ = 

19.1// 2 + DT, or /(sq. Fn.) = 0.132677 2 -eZ)7\ For steel plates /=45 000to 
50,000, or taking strength of riveted joint as 36,000 and safety factor of 4. 

/aafo^.9,000. To find T at any section, measure H from top of chimney 
to section and substitute in formula. 

Total wind pressure P 1 = 25777) lbs., or, if H and D are expressed in 
inches, = 0.1736/id lbs. Resistance to breaking at foundation = 1 .57db 2 tf 
s-h, where db, t, and h are inch equivalents of Db, T, and //. For 

stability, make Df (of foundation) =i//= 2 ^^+10. Moment of wind 

pressure = Pj (0.57/+ /7/). Let W = total weight of chimnev, lining, and 
foundation, in lbs.; then, x, or the lever-arm of IF, = P,(0.5/7 + Hr) -f- W 
If x<0.5Df, the structure will be stable. (0.57)/-= x = factor of stability! 
usually about 1.6, but increased to 2.5 and even 3 for loose soil.) t should 
never be taken less than | to ^ in., to insure durability, rivet diam., dr. 
not less than £ in., spaced about 2.5 dr (c. to c.), and in any case <16f . 
(1 cu. ft. of foundation weighs 125 to 150 lbs ) 

Foundation bolts (usually 6 or 12): Gross overturning moment = 
12.577&77 2 ; moment resisting overturning -=0.5W ] Db (where W l = wt. of 
shell), and net overturning moment P = 0.5P&(25772— TFi). If P r = diam. 
of bolt circle, then Tc (or overturning moment at Dc) = 0.5Dc X 9,000 lbs. X 
No. of bolts X area of 1 bolt in sq. in. (7T = DcT = Db). 

Lining: Where temperatures are above 600° F., fire-brick linings are 
used. Linings are generally 9 in. thick for lower 30 ft. of stack, and 4 in. 
thick above that height. 1 cu. ft. brick (red or tire) weighs about 120 lbs 







168 


APPENDIX. 


ENERGY AND THE TRANSMISSION OF POWER. 


Screws for Power Transmission (Screw-Presses, etc). Square 
threads are preferable to V threads, and the moment to raise load IV 



p" -V 2 tTh 

2 7tr—p"p 


) 


9 


where r = mean radius of thread, p" = pitch, and /i = coeff. of friction be¬ 
tween nut and screw. Let n = No. of threads in nut, the projected area 
of which = 0.7854n(d 1 2 — d 2 ~), and \V = 0.7854np(di 2 — d 2 2 ), where d x and d 2 
are root and outer diams. of thread, and p = allowable pressure.in lbs. per 
sq. in. of projected area, = 125,000 V, where F = rubbing speed in ft. per 

min. and ^100. (p = 80,000 = V when F = 400.) These values of p are 
for W. 1.; for steel, multiply same by 1.2. p = 0.07 for heavy machine- 
oil and graphite in equal vois., =0.11 for lard-oil, =0.14 for heavy machine- 
oil. 

Efficiency: Let a = pitch angle at radius r, (tan a — p"-^-2r.r), and = 
angle .of friction, (tan <£ = /x). Then, efficiency = tan a -s- tan (a + <f>). For 
max. eff., make a = 45° — 0.5<£. In order that load may not overhaul, a 
must be less than <£, and the efficiency cannot then'exceed 50%. 


Piston-Itods, Connecting-Rods, Eccentric-Rods. 


Euler’s formula for compression (both ends free) is : P = x 2 EI -r-l 2 , where 
P = total pressure or load in lbs., 1 = length of rod in in. (/ = ^d 4 -v-64 for 
circular sections; / = 6 3 6 h- 12 for rectangular sections). 

Substituting in formula, introducing a factor of safety s, and taking E = 
29,000,000 for W. I. forgings, P = 29,000,000 d 4 = 2s/ 2 for circular sections, 
and P = 23,800,0006 3 6-^s( 2 , where d = diam. in in., 6 and 6 = breadth and 
height in in.,— d, 6, and 6 being taken at mid-length. For piston-rods, 
s = 8 to 11 when load fluctuates between P and 0; s = 15 to 22 when load 
fluctuates between + P and — P. (For very large horizontal engines the 
deflection of rod due to weight of rod and piston should be considered, 
and it should not exceed 0.15 in.) For eccentric-rods s = 40, for connect' 
ing-rods s = 25 and 15 respectively for circular and rectangular sections. 
h at mid-length = 1 756 to 26 (heights at crank and cyl. ends = 1.26 and 
0.86, resp.). d tapers to 0.8d at crank end, and to 0.7 d to 0 75d at cyl. end). 
For very low speeds (circ. section) s = 33; for sudden changes in direction 
of P (as in pumps), s = 40 to 60. For high speeds, as in locomotives 
(rect sections), 6 = 26 s = 6.6 to 3 3 (See also Columns, Euler’s formulas, 
ante.) 

Connecting-Rod Ends (Marine type, rod formed with a T-end, brasses 
being held to T by bolts and cap). Diam. of each bolt at bottom of thread, 

d = 0 02 A '/p, where P = £ max pressure on piston in lbs. Thickness of 
cap and T on end of rod, t=lAd. These values of d and t are for W. I.; 
for steel take 90% of same. 

Piston-Rings. Radial depth, 6 = 0.033d when bored concentrically, 
= 0.04 d opposite joint when bored eccentrically (tapering to 0.76 at ends). 
Width = 26; overlap of ends = 0.1d, where d = diam. of cyl. 

Stuflflng-Roxes. Inner diam. of box = depth = d+(0.8 to l) y /~d, 
where d = diam. of rod 

Pedestals (d = shaft diam., ? = leneth of brass, both in in.). Diam. 
of bolts for base and cap = 0.25d +0.125 in.; (list. bet. centers of cap-bolts 
= 3.3d + 1.65 in.; do., base-bolts = 3. 5d + 1.75 in.; width of nedestal = 0.72Z. 
Thicknesses: cap, 0.375d; base-plate, 0.25d + 0.125 in.; metal around cap- 
bolts and brasses, 1.8d + 0.09 in. (If d<7 in., use 4 bolts each for base 
and cap.) Brasses: thickness at center = 0.08d +0.125 in.; do., at sides, 
0.06d + 0.09 in. 

Journal Hearings. 

Allowable pressures (p) per sq. in. of projected area ( iXd ): 

Journal. Bearing. p. 

Crucible steel (hardened) Crucible steel 2,100 lbs. 

“ (hardened) Bronze 1,250 

“ “ (soft) “ 850 



APPENDIX. 


169 


Journal. 

Wrought iron, polished 
W. I. orC. I. 

< ( (t it 

W. I. (water lubrication) 


Bearing. 

Bronze 

i i 

C. I. or bronze 
Lignum Vitae 


Crank-pin 
• * 

Cross-head pin 


Speed. 
Moderate 
High 
Moderate 

Main bearings, 

Crank- and cross-head pins, locomotives, 
Crank-pin for punch and shears, 

Main rods of locomotiv e s, 


V. 

570 

425 

350 

350 


900 

550 

1,100 

700 

200-350 

1,400, 2,100 resp. 
2,800 and up 
(Bach.) 
1,800-2,100 
350 
300 

1,000-1,500 


Freight-car axles, j , , ~ ( 

Passenger-car axles, s 
Neck bearings of sheet-mill rolls, 

(Eng’rs Soc. of W. Pa., Dec. ’05.) 

Main bearings of engines, c + \/^~ 

0 = vel. of rubbing surface in ft. per sec.; e = 500 for vertical 
engines, =375 for horizontal. (Edwin Reynolds.)1 
pi <50 000; p = 30 to 80 lbs.; F = 400 to 1,200 ft. per min.; Z = 3d 

S^fe'n diam for oil-film = 0.001 (d+1) in. for d<5 in. Allowance =' 
0.001 (d + 4) in. for d> o in. (Gen. Elec. Co. Practice ) 

Thrust-bearings: pV = 40,000 to 50,000, with loads up to 1,000 lbs per 
sq. in. of projected collar area. 

Worm-genrs: pV = 60 000 to 75,000 for max. efficiency, the higher value 
for high values of F, and where helix angle = 20°; worm of hardened steel 
wheel of phosphor-bronze. For electric-elevator work F = 600 to 1 000 ft 
per min. 

Large shaft-bearings tested by the Westinghouse E. & M. Co., over runs 
ol 7 hours yielded the following unusually high values for vV' 9-in shaft 
150,000 to 500,000; 15-in. shaft, 260,000 to 840,000 (p = i 40 To 170) 

Lower values for each size were when heavy machine oil was used higher 
values with paraffin oil. (A. S. M. E., Dec ’05 ) 

Friction Couplings (C. I.). Shaft diam. = d; hub diam. = 2d; depth 
i -^ IOOVe ~e ’ width of groove = £d; width of friction-cone faces = lid; 
thickness of wheel webs = $d; angle between shaft and cone faces = 4° 
to 10°. 

Claw Couplings (C. I.). Diam. of both claws, D = 2.1d + 2 in.; diam 
of fixed hub = 1.6d + 1.6 in.; length of fixed claw = 0.9d+l in ; depth of 
recesses in both claws = 0.6d +0.6 in.; length of fixed hub = 0 5d + 0 5 in • 
length of sliding claw = 1.7d +1.7 in. (of diam. D throughout length)- depth 
of groove midway between end and recess = 0.3d + 0.3 in.; width do = 
0.5d + 0.5 in. (d = diam. of shaft). 

Roller Bearings. For heavily loaded, slow-running journals P = 
2,100 nld for hardened-steel rollers (Ing. Taschenbuch). 

The coefficient of friction for roller bearings is from 0.2 to 0.33 of that 
of plain bearings. (C. H. Benjamin, Machinery, Oct. ’05.) 

Mossberg bearings (rollers confined rigidly as possible in a cage): Safe 
load in lbs. = craZd, where e = 250 for rollers up to | in. diam. (c = 300 to 350 
for larger rollers). Z (generally) = 1.5Xshaft diam. D. For D up to 12 in 
diam of roller d = 0.104D; above 12 in., d= If to 14- in. n (approx ) = 
27 —(1.6-nd) for d<H in.; n = 90-(80-t-d) when d>1± in. Take nearest 
even number. 

Ball Bearings. Max. allowable load on one ball in lbs., P = cd 2 . Falues 
of c: For C. I balls between two planes, c = 35; steel balls oh plane, coni¬ 
cal, or cylindrical surfaces, c = 700 to 1,000; steel balls in races whose radius 
of curvature = fd, c= 1,400 to 2,100. Above values for continuous use; 
for intermittent use c = twice lower values given (d = diam. of ball in in )' 
Total allowable load on bearing = 0.2PX No. of balls. (Bach and Stribeck ) 
According to C. G^gauff {L’Industrie Electrique, 7-25-’05) the least 
power is_lost in friction when d=tD-r-7)+0.08 in., where D = inner diam 
of race in in. Max. allowable load in lbs. for an annular bearing P = 
84,000/) -s- (ND + 375), where A r = r.p.m, 




170 


APPENDIX. 


For a 2-point bearing, the coeff. of friction, /t = 0.0015; for 3-point, 
0.003 to 0.006; for 4-point, 0.015 to 0.06 (which is no better than a piam 
bearing). The friction loss is constant up to linear speeds of 2 - 000 i t ^ p ^ 
inin. Above 17,000 r.p.m. centrifugal force causes the balls to slide on 

the shaft instead of rolling. __ r i a 

JJevel Gearing. 0 = angle between shafts = a + 0, where « and are 
angles made by the shafts and elements in their respective pitch cones 
fa for larger gear). Let <£ = l80°-tf, and r = angle it o be added to a and 
0 to give face angles of gears Then, if 6 < 90°, tan 0 = r + [r cot 6 + (R - sin 0)L 
if fl = 90° tan a = n + N; if 0>9O°, tan 0 = r + [(R + am 4>)-r cot 4>l « = 

(9-/?; tan r = sin 0 + O.5n. Face angles = a + r and j8 + r for 
smaller gears respectively L> = D x + I >2 cos «; .d-di +£>2 cos 0.( , 

outside diams ' Di d, = pitch diams.; Z ) 2 = working depth of tooth, It, r 
pitch radii ( = 6.5 D u 6.5 d x ); N, n = No. of teeth. Capital letters for larger 

ge The cutter for larger gear should be the proper one to cut N x teeth, 
when! A, = 7 V-s-cos «; for smaller gear, the one to cut » x teeth, where «i = 

71 Spiral Gears. Let angle that teeth make with a line parallel to axis 
of gear = 0. Then, normal pitch r = p" cos 0 (where p —circumferential 
pitch) and p" = r-ecosA Let Pd = diametral pitch, A = No. of teeth in a 
spur-gear of pitch radius r, and JVi = No. of teeth in a spiral gear o Pitch 
radius r. Then, N = 2rPd, and N x = 2rPd cos 6. Pitch diam. = N^Pd cos 0, 

outside diam. = pitch diam. + (2-r-Pd). . , . , • 

The teeth of spiral gear should be cut w r ith a spur-gear cutter wind is 
correct for No teeth, where A 2 =(No. of teeth in spiral gear) . cos 0. 
r and r, (page 50) =(90° -0) and (90°-0i) respectively. . 

Worm-Gears. Involute gears of more than 27 teeth, and having ad¬ 
denda of 0.25p", yield favorable results for pitches not exceeding 18 . 
Allowable pressure on teeth, P(in lbs.)=c 6 p", where 6 — width of tooth in 

in and v n ~pitch in in. , _ . i i j 

c = 250 to 400 for cast-iron ( = 450 to 700 for phosphor-bronze wheel and 

lla \Vorms whose threads make an angle >12.5° with a normal to axis of 
worm generally run well and are durable. (Halsey.) , , 

Diam of worm wheel at throat = 0.3183 X (No. of teeth + 2) X pitch of 

*°Power in Transmitted by Worm-Gearing. p 4 = (aF 2 + bF + c) = N, foi 
single thread, where p = pitch of teeth in worm wheel in in., t - H-P- trans¬ 
mitted, and N = r.p.m. For F> 3 H P., a = 4.74, 6 = 113, c=-105; foi 
p o yi p a — 29 6 = 25 c = 2 

For double, treble, and quadruple threads take 2N, 3N\ 4A respectively 
for denominator of formula. Greatest pitch diam of worm, d — 17.2p . r , 
for single thread. For double, treble, or quad, threads multiply formula 
value of d for single thread by 2, 3, or 4 The foregoing is for finished 
worms and gears; if rough, cast teeth are used, multiply values of p and d 
obtained from formulas by 1 33 and 0.8, respectively. (Derived from 
practice of Otto Gruson & Co., as stated by W. H. Raeburn, Am. Mach., 

4 Flat-Link Driving Chain (Steel). Load in lbs. = P; end diam of 
pin, d = (2.4P + 6,100)+ (P + 27,000); diam of pin bet hnks = 1.25d for 
small sizes (ranging to 1.12d for large sizes); width of link - 5d, lengt 
of pin bet links = 1.65d +0.22 in. (for d<l in.), or 2.62ri-0.7 in. (for d> 

1 in.); length, c. to c. of pins = 2.7d + 0.l6 in.; over-all length of hnk = 
4 4j_l’o. 16 in. No of plates, i(hi on each side): 

When P= up to 1,000 lbs. 1,000 to 4,500 4,500 to 13,000 

2 4 6 

Thickness of each plate = (3.17P + 3,900) -vt(P + 29,000) 

(Derived from data on a chain extensively used in Germany.) 

Pulleys (Cl) Width of face, 6 l = (l.lXbelt width)+0.4 in.; 
ness of rim at edge = ( 0.01 Xradius of pulley) +0.12 in. Crowning: 
of pulley at center is 0 . 12 ^ 6 , greater than diam. at edges. No. of arms = 
0 7 \/d For oval arms h (long axis of ellipse) =^1.256<d-i-No. of arms. 
h, (short axis) = 0.46. h and h x (at hub) taper to 0.86 and 0 . 86 , at rim 
(b -belt width, < = belt thickness, d = diam. of pulley,—all in in ). Length 
of hub = 6 i when 6 , > 1.2 to 1.5Xshaft diam. (for narrow faces); for wide 


larger 

8 


thick- 

diam. 




APPENDIX. 


171 


may T j 3 ? * ess t ! ian &i For loose pulleys make length of hub = 
2 Xshaft diam. If 6j>12 in., use two sets of arms. 

Pulley Blocks and Sheaves. Diameters are taken considerably less 
in hoisting work than for power transmission. The Ing. Taschenbuch 
gives the following: Diam. of sheave = cXdiam. of rope, where c = 20 for 
wire rope and 8 for hemp. 

♦ Brakes (Fig. 40). Let 17 = pressure on brake lever in lbs., P = brak- 
'ng force at rim of wheel in lbs., /i = coeff. of friction < 0.5 for wood or 
leather on iron (dry surfaces) =0.18 to 0.25 for iron on iron, diminishing 

with increase in vel. For block brakes (I.) I7 = ~^-(—±—) theminns 
sign being used for rotation indicated,—plus for opposite. For 5 = C = ^ 



Fig. 40. 


17 = 0, or the brake is self-acting; P = C is therefore made>/<. For dotted 
position, C is negative and signs in parenthesis should read . For opp. 
direction of rotation, B-i-C should be < /i. 

Band Brakes: Let e = base of hyperbolic system of logarithms = 2.71828; 
« = angle spanned by the arc of contact of band with wheel; t and b = 
thickness and width of band, and f t = allowable unit stress in band. Then 
(in II.) tension 7 1 = P = (e/<« — 1); and t = Pe/'o'= (e/^« — 1 ), for direction 1 (for 
direction 2, interchange values of T and t). Band cross-section = 6 t = 
PePB-TrftiePa — 1 ), where /, = 8,500 to 11,000 lbs. per sq. in. (t is generally 
about 0 15 in.,— b not more than 3 in.). If n is taken = 0.18 and «-=-2^ = 0.7 
(generally), then P = 0.83P and t = 1.83P, for direction 1. 

For <* = 2* = 0.1 0.3 0.5 0.7 0.9 

=1.12 1.40 1.76 2.21 2.77 

In II, T7 = 7Y7 = A;in III, W = tC+-A. 17 is least when end with lesser 
tension is attached to lever, as T in II (direction 1) and t in III (dir. 2). 

Differential Brake (IV): 17 = (TC — tc)-*-A — P(C — ce^«) = A(e/ £ « — 1 ). 

If C = cel Jor , 17 = 0; C is generally taken >ce/ la . (For a = 2^ = 0.7, C = 2.5c 
to 3c.) For alternating directions of rotation (V), I7 = PC(e/ ,a -f 1 ) -s- 
A(eMa — I), A block brake is preferable to this arrangement. 































172 


appendix. 


HEAT AND THE STEAM-ENGINE. 
Properties of Saturated Steam (below Atmos. Pressure). 


p, abs. 

t° F. 

V. 

w. 

H. 

h. 

0 

L. 

.089 

.125 

.25 

.50 

.75 

1 . 

2. 

4. 

6. 

8. 

10. 

12. 

14. 

14.7 

32. 

40. 

59.5 

80. 

92.5 
101.99 
126.27 
153.09 
170.14 
182.92 
193.25 
201.98 
209.57 
212. 

3,387 

2,717 

1,270 

640.8 

442.5 

334.6 

173.6 
90.31 
61.67 
47.07 
38.16 
32.14 
27.79 
26.42 

.0002952 
.0003681 
.0007874 
.00158 
.00226 
.00299 
.00576 
.01107 
.01622 
.02125 
.02621 
.03111 
.03600 
.03794 

1091.7 

1094.2 
1100. 

1106.3 
1110. 
1113.1 

1120.5 

1128.6 

1133.8 

1137.7 

1140.9 

1143.6 

1145.8 

1146.6 

0 . 

8. 

27.5 
47.8 

60.5 
70. 
94.4 

121.4 

138.6 

151.5 

161.9 

170.7 
17-8-3 

180.9 

1091.7 

1086.2 

1072.5 

1058.5 

1049.5 

1043.1 

1026.1 
1007.2 

995.2 

986.2 
979. 
972.9 
967.5 
965.7 


Superheated Steam. According to Linde (Z. V• D 28. ’<g) 

the PV law may be expressed as: 144 p(v + 0.261)-85.8b., ™ here £ /° s - 
Pressure per sq in., v = cn. ft. in 1 lb. at the pressure p and t = absolute 
temperature in degs. F A formula which ex P r || s | s the results of his 

experiments to determine k v is: k p = 0.462 + P ( T _ 135 _ °- 00022 ) , p and r 

as above Herr Berner (Z. V. D. I., 9-2-’05) states that Linde’s values 
for £ are confirmed by his own observations, those of Lorenz being from 
‘>0 to 25% too high He further states that the cost of lubrication is 
slightly higher than when saturated steam is used, that the resistance to 
flow in a fuperheater coil = 1.2 X resistance of smooth pipe, and that the 
resistance of a valve fully open is equal to the resistance of about 55 ft of 
smooth pipe. The velocity of flow in engine Passages may be as high as 
12 000 ft per min. (Arndtsen, Z. V. D. I., 11-25 05.) 

Corliss halves, Dash-Pots. Diam. of valve = c X cyl • diam,, where 
c = 0 25 for valve on high-pressure cyl. ( =0.2 for low-pres. cyl.). Dash-pot 
diameters are about 0.8 of the diams. of their respective valves. 

Steam Consumption of Compound Engines, high-grade, at full load 
= 15 6 lbs per kilowatt-hour ( = 11.5 lbs. per H.P.-hr.) at 170 lbs gauge 
pressure, 90° F. superheat, and 26 in. vacuum. (Averages by Stevens <1 

^ Prime Movers for Power Plants. In a high-grade power plant about 
10 3 % of the heat units in a pound of coal are delivered to the bus-bars in 
the form of electricity It is possible to raise this thermal efficiency to 
about 14.4% (with steam-turbines to 15%) by reducing the losses due to 
the stack, boiler radiation, and leakage, and by using superheated steam. 
Where the load-factor exceeds 0.25. economizers should be used. Auxil¬ 
iaries should be steam-driven with exhaust heater The^fnctmnHoss 
of a 7,500 H P engine recently tested was 6 35% of the H.P. generatea. 
Large gas-engines can convert about 24% of the energy of coal into electric 
energy the chief objection to their use being with regard to overloads. 
This objection may be overcome by a suggested combination of gas-engines 
and steam-turbines (utilizing the waste heat of the gas-engines in the pro¬ 
duction of steam), which would yield an average thermal efficiency ot 24.5%. 

Comparative cost of maintenance and operation of plants per kw.-lir.. 


Steam- 

engines. 

Maintenance and Operation 100 
Relative Investment 100 


Steam- 

turbines. 

80 

83 


Gas- 

engines. 

51 

100 


Gas-engines 
and tur¬ 
bines. 
46.3 
91 

























APPENDIX. 


173 




Marine Steam-Engines. 

The Screw Propeller. The pitch of a screw is the distance which any 
point in a blade will advance in the direction of the shaft or axis during 
one revolution, the point being assumed to move around the axis and 
without “slip.” Propellers are generally provided with four blades (naval 
vessels and small high-speed boats with three). The blades are generally 
inclined backward from the vertical from 8° to 20° (according to the r.p.m.) 
in order to throw the water to the rear and to increase the efficiency. 

The indicated thrust of screw, T= (I.H P. X33.000) -s- NP, where N = 
r.p.m., and P = pitch in feet. The mechanical efficiency of the shaft trans¬ 
mission varies from 0.8 for engines of about 500 H.P. up to 0.95 for large 
ones. The mechanical efficiency of the screw = Useful work of axial 
thrust-5-Shaft perfor mance = 0. 6 to 0.7 for best conditions. Diam. of 

Screw in ft., D — i£ v I.H P. -s- (0.01.PV) 3 ; Total area of blades (developed) 

= XjV I.H.P.-i-iV; P varies from 0.9D to 1.5D. Speed V is measured in 
knots (1 knot = 6,080 ft. per hr.). 



V. 

K. 

K 

1 • 

Cargo Boats, 

8-13 

17-19 

19- 

15.5 

Passenger and Mail Boats, 

13-17 

19.5-21.5 

15- 

12.5 

Do., very fine lines, 

17-22 

21-23 

12.5- 

9 

Naval Vessels, 

16-22 

21-23.5 

11.5- 

7 

Torpedo Boats, 

20-26 

25 

7- 

6 


The Apparent Slip (in per cent) <S = (C— V) -t- 100C, where C = PX60iV-5- 
6,080. S=-2 to +8 for slow freighters, =8 to 15 for passenger and 

mail steamers, =13 to 20 for naval vessels, =20 to 27 for small, fine-lined 
boats. 

Strength of Blades:—The indicated thrust T (divided by the number of 
blades Z ) acts at a distance 0.3 5D from the center of shaft and causes a 

T 

bending moment Bm- Bm = ^-(0.35D — distance from c. of shaft to root of 

blade). For a parabolic segmental cross-section (length l, thickness h) 
oblique to axis, the Moment of Resistance — 0.076lh 2 , and consequently 
f = Bm + 0.076lh 2 . f (safe) in lbs. per sq. in. = 7,800 for cast steel, =5,700 
for bronze, =2,800 for C. I. 

Thickness of blades at tips = 0.25 to 0.8 in. for bronze, and 0.6 to 1.2 in. 
for C. I., according to size of the screw. 

Indicated Horse-Power of Engines. I.H.P. = p m La(2N) j- 33,000, 
where a = area of low pressure cyl. in sq. in. pm, the mean effective pres¬ 
sure, depends on the absolute boiler pressure p, and also on the number of 
expansions: 

, / , T\ . vol . of steam admitted into h. p cyl. 

p m -kpc{ l+Iog.-j. where c = 1. p. cyl. vol. + h. p. cyl. vol. " • 

k has the following values at ordinary speeds: 


Compound-Engines, 0.65 to 0.7 (at higher speeds, 0.6 to 0.65). 

Triple-Expansion, 0.55 “ 0.6 (. 0.52 “0.58). 

Quadruple-Expansion, 0.52 “ 0.54 


Total Number of Expansions ( = l-f-c): Compound, small boats, 5 to 6; 
do., freighters, 7 to 8. Triple-Expansion, torpedo boats, 5 to 7; do , naval 
vessels, 6.5 to 8; do , express and freight steamers, 8 to 10. Quadruple- 
Expansion, express steamers, 10; do., freight steamers, 11 to 13 Cut-off 
in high-press, cyl. is at about 0.7 stroke (0.6 stroke for slow boats). 

Piston Speed and Revs, per Min. 


Torpedo Boats, 

Armored Vessels, 

Express Steamers, 

Large Passenger Steamers, 
‘ * Freight 

Small 


• 4 


41 


Speed, ft. per min. R.P M. 

1,000-1,200 300-400 

800-1,000 100-150 

800- 950 75- 95 

700- 900 70- 90 

700- 800 70- 85 

600- 750 95-130 

400- 600 150-200 


passenger 





174 


APPENDIX. 


Steam Velocities (ft. per min.). Main steam-pipes, 6,000-8,000; 
steam passages: h. p. cyl., 5,000-6,000; intermediate cyl., 6,000-7,000; 
1. p. cyl., 7,200-8,500. For exhaust take 80% of above values. For small 
engines these velocities may be increased 20%. 

Cylinders. Thickness of walls (cast iron) / = - —bO.4 in., 

5.120 + 10p 

where p = gauge pressure in lbs. per sq. in at h. p. cyl., and d = diam. of 
h. p. cyl. in in. (This value of / is for h. p. cyl. with or without jacket 
and also for intermediate and 1. p, cyl. linings. Cylinders without linings 
should be 0.2 in. thicker to allow for reboring.) 

Thickness of cylinder head t\=t (for cast iron, head ribbed) = 0.6/ to 
0.65/ for cast steel. Diam. of cyl.-head studs = <; pitch of studs = 3/, 
5.5/ and 6.5/ for high, intermediate and low-pressure cylinders, respectively. 
Thickness of cyl.-head flange = 1.2/, width = 2.6/ to 3.3/. 

Relief valves (for both heads) should have a diam. = ( I 1 2 , T V, 2 , ?T )Xdiam. 
of (high, intermediate, low-pressure cyl.). Valves should open at about 
8 lbs. above p. 

Pistons. (Cast steel, coned, concave toward crank). Thickness near 

center, / = 0 . 0043 dv p -f r - thickness near rim = 0.5/ to 0.7/. 

c = 0.24 in., 0.36 in., 0.48 in., respectively, for h., i. and 1. pres. cyls. 
p = boiler pressure in lbs per sq. in. for h. p. C yl., = 0 45Xboiler pressure 
for intermediate cyl. , = 0.2 X boiler pressure fori, p.' cyl. For forged steel 
take •£• of above formula value for /. 

Piston-Rods. (Medium hard steel, end tapered and fastened to head 
by nut.) Area at root of thread in sq. in. > (pXarea of h. p. cyl. in sq. in.) 
-t- 7,000. (For naval vessels and torpedo boats substitute 10,500 and 
12,500 respectively for 7,000). Full section of rod beyond taper = 2Xarea 
at root of thread. 

Connecting-Rods. Length = (2 to 2.25) X stroke. Diam. at piston 
end = diam. of piston-rod, approx.; diam. at crank-end = (1.1 to 1.4) X 
diam. of piston-rod, according to length. 

Rearings. The crank bearing is lined with white metal of a thickness = 
(0.025Xdiam. of bearing)+0.2 in. Thickness of cast-steel bearing cap 
at the middle = (0.17 to 0.24)Xdiam. of bearing. Shaft bearing: thick¬ 
ness (cast iron) = 0.12d + 0.2 in.; for bronze, thickness = 0.09d + 0.12 in. 

Thickness of white-metal lining = (o.2 + ^_)in. d = shaft diam. in in. 


Crank-Shafts (forged steel): 


d 3 = 


16 


Trn 

T 


(i-* 4 y 

' d* / 


where 


d = outer 


diam. of shaft in in. (d) = inner diam. in case of a hollow shaft), T m = 
turning moment in inch-lbs. = 63,025X I.H.P. = N. 

f safB (average) in lbs. per sq. in. = 6,600 for torpedo boats, =5,700 for 
naval vessels, =4,500 for mail steamers, =4.000 for freighters (max. and 
min. values are equal to average values±10%). 

Crank-Throws. Outline described in part by circles (of diam. = 2d) 
from centers of shaft and crank-nin, connected" with filleting curves of 
radii =d. (d = diam. of shaft). Thickness of throws = 0.6d to 0.7 d. The 
shaft is enlarged -fa of its diam. in the throw. Thickness of flanges on 
shaft = 0.25d to 0.28d. Length of bearing = diam. of shaft = 1 4 to 1 6 
for torpedo boats, =1.1 to 1.4 for naval vessels, =0.9 to 1.2 for other 
vessels. 

Surface Condensers. Cooling surface in sq. ft. required per T H P • 
Compound, 5 to 6; triple-expansion, 3.5 to 5; quadruple-expansion, 3 5 to 
4.6: toroedo boats, 26 to 32. (The lower values given are for naval ves¬ 
sels.) Condenser tubes are of brass, tinned inside and out, £ to £ in. out¬ 
side diam. and about 0.04 in. thick. 


Air-Pumps for Surface Condensers (Single-acting). Volume = cX 
vol. of 1. p. cyl. c = tV to tr f°r compound; = to for triple-expan¬ 
sion; = 5 ^ to for quadruple-expansion. For injector condensers. Vol = 
(* to *) X vol. of 1. p. cyl. 

Surface Condensers of High Efficiency. By passing the condensing 
water several times through the tubes (arranged in groups), and by pro¬ 
viding for the thorough drainage of the water of condensation so that 
the tubes are not contioually subjected to showers of water particles which 




APPENDIX. 


175 


impair the surface contact, Prof. R. L. Weighton has designed condensers 
to be used in connection with dry air-pumps which condense 20 lbs. of 
steam per hour per sq. ft. of surface, condensing water required being 
21 times the amount of feed-water used. He has effected a higher sur¬ 
face efficiency—30 lbs. per hour per sq. ft.,—but the condensing water 
required in this case is equal to 28 times the feed-water. Vacuum in 
both cases is 2S.5 in. of mercury, feed-water temp, at inlet = 50° F. For 
a system with tight piping, capacity of air-pump = 0.7 cu. ft. per lb. of 
steam condensed per hour. The condenser tubes are provided with tri¬ 
angular wooden cores in order that the water may meet the tube sur¬ 
face in thin streams. Temp, of hot-well may be 3° to 5° higher than 
that corresponding to vacuum (up to 29 in.). 

Circulating Pumps l(Double-acting). Vol. =0.025 Xvol. of 1. p. cyl. 
(approx.). 


Boiler Accessory Apparatus. 

Feed-Water Heaters. Let t and T = initial and final temperatures of 
water in degs. F. [average temp. = (t + T) -5- 2]. B.T.U. transmitted per 
sq. ft. of surface per hour, per degree difference of temp. =c = 180 for 
water-tubes, 200 for coils, and 114.5 for steam-tubes (usually 2 in. diam.). 
Let 2’8 = temp. of exhaust ( = 212° F. generally); then, B.T.U. per hour 
per sq. ft. = c[_Ts— 0.5^ + T)]; lbs. steam condensed per sq. ft. per hour = 
c[T 8 -0. 5(t +- 2')]-=-966. Velocity of water in tubes in ft. per min.: single- 
flow, 8.33; double-flow, 12.5; coils, 140. Sectional area within shell = 
cX total cross-section of tubes, where c = 6.3 to 9 for water-tubes, = 7.5 to 
10 for steam-tubes,—-the higher values for variable loads. For coil heaters, 
sectional area within shell = (11 to 8) X cross-section of exhaust pipe, 
inversely according to the capacity of heater. Open heaters with trays 
or pans: Volume of shell in cu. ft. = Capacity in H.P.h-c, where c = 2.2, 
6, and 8 for very muddy, slightly muddy, and clear water respectively. 
Tray surface in sq. ft. = lbs. water heated per hr.-5-c, where c=118, 166, 
and 500 for very muddy, slightly muddy, and clear water respectively. 
These values for tray surface are for vertical heaters; for horizontal 
type of heater the values of c are about 8% lower. 

Siphon or Barometric Condense rs operating on the principle of in.iec- 

tors: Diam. of exhaust pipe in in., d = V c X lbs. steam to be condensed per min., 
where c = 0.81 when wt. of steam is less than 20,000 lbs. per hour ( = 0.63 

if greater than 20,000 lbs. per hr.). Diam. at throat in in. = w = 1 7,210; 
width of annular opening through which water is admitted = Ww -5- 39,550d 
(IF =lbs. steam to be condensed per hr., tc = lbs. water required to con¬ 
dense 1 lb. of steam). 

Air-Pumps for Stationary Engines. Single-acting: vol. m cu. ft. = 
0.032*8-5-AT; double-acting: vol. in cu. ft. = 0.016*S-5-A r . <S = lbs. of steam 
condensed per hour, and iV = r.p.m. (Ing. Taschenbuch.) 


Locomotives. 


Elevation of Outer Kail on Curves. E (in ft.) = 0.06688(7F 2 -5- R, 
where G = gauge of track in ft., V = velocity of fastest train in miles per hr., 
and A! = radius of curve in ft. (It. R. Gazette , 3-16-06.) 

Combustion. 


Natural-Gas Fuel for Steam-Boilers. The same economy is ex¬ 
hibited with a blue flame as with a white or straw-colored flame, but the 
latter affords greater capacitv. One boiler H.P. may be expected from 
43 to 45 cu. ft. of gas (at 60° F. under a pressure of 4 oz. above 29.92 in. of 
mercury). Fuel costs are the same with natural gas at 10 cents per 1,000 
cu. ft. and semi-bituminous coal at $2.87 per ton of 2,240 lbs. (J. M. 
Whitham, A. S. M. E., Dec. ’0o.) . 

Efficiency of Combustion. The higher the percentage of ( (J 2 m the 
eases escapine into the chimney, the higher will be the efficiency of the 
furnace, and the production of C0 2 may be foried until the presence of 
CO indicates incomplete combustion. In good furnaces 10 to lo / 0 ot CU 2 




176 


APPENDIX 


may be realized The approximate fuel loss (in per cent) due to incom¬ 
plete combustion = 0.4(^2 — <i)-=- (per cent by volume of CO2), where t 2 = 
temp, of chimney gases and <1 =temp. of air entering the furnace (both in 
dogs. F.). An instrument called a CXb recorder indicates and records con¬ 
tinuously the percentage of that gas present 

Mechanical stokers do not accomplish any marked saving of fuel over 
careful hand firing in plants where less than 200 tons of coal are used per 
month, but they yield much better results than average hand firing, are 
easily forced, maintain a uniform steam pressure, and assist greatly in the 
smokeless combustion of soft coals. They are adaptable to all kinds of 
solid fuels, and in this respect promote economy, for it often happens 
that a cheap, low-grade fuel may be employed, whereas with hand-firing 
a more expensive quality would have to be used. 

Incrustation and Corrosion. 

Boiler Purges. Caustic soda and lime-water combine with the car¬ 
bonic acid contained in water (in combination as bicarbonates) and pre¬ 
cipitate calcium and magnesium carbonates. Soda ash acts on the bicar¬ 
bonates of lime and magnesia, forming bicarbonate of soda, which is 
decomposed by heat into C0 2 and sodium carbonate, the latter being 
precipitated. ' 

Sodium aluminate and sodium fluoride are also used in waters contain¬ 
ing bicarbonate of lime. 

Trisodium phosphate is used where water contains sulphate of lime, 
precipitating sodium sulphate and calcium phosphate. 

Internal-Combustion Engines. 

Gas Producers are closed furnaces in which the fuel is burnt with a 
limited supply of air and steam, resulting in the production of gas. The 
air and steam are either forced (pressure producer) or drawn (suction pro¬ 
ducer) through a bed of incandescent coal or coke. The O of the air first 
combines with the C of coal to form COo. This passes up tnrough the 
incandescent coal and changes to CO. When steam is mixed with the 
air and meets the burning fuel, H is liberated and the O of steam com¬ 
bines to form more CO. These, with the N of air and the volatile part of 
the fuel (CH 4 ) make up the resulting fuel-gas. Theoretically the best 
temperature is about 1,900° F. 1 lb. of coal with upwards of 0.7 lb. steam 
■will yield from 65 to 75 cu. ft. of gas (135 to 140 B.T.U. jjer cu. ft.). Pres¬ 
sure producers are used for engines of over 200 H.P. Fn Fhese the air and 
steam are furnished under a pressure of from 2 to 8 in. of water. The hot 
gas passes through an economizer where it preheats the air used and also 
gives up heat for the generation of the steam required. It then passes 
through the scrubber (vessel provided with trays of coke upon which 
■water streams from above) and thence to the purifier (another vessel pro¬ 
vided with trays of sawdust, and also with oxidized iron-filings when sul¬ 
phur is to be removed from the gas). The best results are obtained from 
anthracite (pea size or larger) having less than 10 to 15% of ash and but 
little moisture If the fuel contains more than 5 to 8% of volatile matter, 
it will cohere and prevent proper working of producer. Coal with an ex¬ 
cessive amount of ash tends to choke up the air-passages. 

Grate surface per H. P. = 6 to 8 sq. in. (the latter for producers of less 
than 25 FT.P. capacity). The volume of producer per H.P. =0.11 cu. ft., 
approx, (firing intervals of 3 to 4 hours), for anthracite, and 0.18 cu. ft. 
for coke. Vol. of scrubber = 0.9 to 1.1 cu. ft. per H.P. Vol. of purifier = 
0.36 cu. ft. per H.P. In ordinary generators about 85% of the heat of 
the fuel leaves the producer, a loss of 15 to 20% being due to heating, 
radiation, and unburnt residue. Efficiency, 65 to 75%. 

Suction-Producer Tests of a number of plants in London using Scotch 
anthracite (pea) showed a consumption of 0.85 to 1.1 lbs. per B.H.P. hr. 
for full load, and 0.9 to 1.25 lbs. at half load (larger values for 8 HP., 
smaller for 20 H.P.). Volume of producers in cu. ft. per H.P. =0.23 (for 
20 H.P.) and 0.26 (8 H P.). R.P.M., 200; mechanical efficiency, 81 to 

84% at full load (69 to 71% at half load). M.e.p. about 79 lbs. 


appendix. 


177 


IIlast-Furnace and Coke-Oven Gases t? 
about 88,000 cu. ft. of blast-furnace m art i;£° r * ea . ch of iron sm elted 

C °Hot Tnhes ab ° Ut - 8 ’ 8 ? 0 CU ft - coke-ovln ga s 6 ' ° n<3 *° n ° f CoaI in 
° n f ° °, 33 lb-«a q soiSe fr ^hoiS 7 ° U ' f ‘‘ ° f illuminatin g gas per hour (or 

a beverage b^tff^dditlon^of 1, wo^XShoT* b"^ S* consum P tion aa 
IS excessive. unpleasant odor unless the percentage of benzol 

(carto 5 > 3 iH 2 r ZSSgST :2(c"H 0 «o)t?(6o;) ioxide - 

alcoholllOT^^dn^thiMn^hfeh no^rf^nt 1 W ' abs °' Ute 

SP % by G ^L ty %^ 1 . A1COh °' S a p‘.T IF - APPr ° X ' L ° Wer Heatia ® Value. 

*95 '93 s SI 6 11.700 B.T.U. per lb. 

90 87 7 10,900 “ ‘‘ •• 

One gal. abs. alcohol = 6.625 lbs. 77’,500 • • «' 

for com bustion°of^Tb U ^1 cofud -9 ?bs 22 Sr + i°ii 3 ? + ° ? 4S0 Air required 
Poiliag-point = 173.1° F.^freezing-pofnt =^—^00^ F U ^ at 62 ° F * 

Specific heat of liquid at 32° F =0 ^47 k > * 

ip i, h T n r~ 1J4 Law of compreasion PF, ;,° f pTM7 0 ' 4634: fe, “ 0 4 l 

cien,l?,alcKl 0 v\po e r1f‘u, d ed UP ^V Wamed -P suffi- 

per H.p. hour, and efficiency ispromoted >7 CT 1 ™!. is abnut 20 lbs. 
nigh as possible. P X 1 by having its temperature as 

Denaturants. 

Methyl LOWe (») ValU e 

Sites 176° F B 'f U. Per lb, 

te.-.::::::::::® oso ° }??: $S8 ■■ •• :: 

Gasal ™. o. 7 oo 180-210 0 iS; 8 gg :: :: :: 

Denatured Alcohol added ,00 yols. of 

French.0^832 *7^5^ C5H5N (^H 6 0 C 6 Hg Gasoline 

Do™‘Motor Spirit ’’: '. .0.825 0.75 0.25 0.25 2 ^ 

t.ure, high temperatures 1 limiting'theanowab!rcXpre t ssi VaPOri f e ? the m - ix ' 
the economy. For a 90% (vo! ) alcohol 7 9 lbJ P^ ess . lon and decreasing 
required for the combustion of'1 lb Assuming n n'li?™, theoretically 
50%) in practice, 1 cu. ft. dry air (at 60° F 1 ;« J.!^ 8 r^i ( an excess of 

alcohol, or as 90% (vol ) = 87 7% (wt 'i 1 ik • *•?, su Pphed for 0.0065 lb 

non7^ iK “r u v 1 NT, ' (wt.), 1 lb. air wi carry 0 877 (1 —11 c\ 

(h0075 lb. of abs. alcohol, and (1-0.877)(1 1 8) = 0 m ik U V 118) = 

If the air be considered as saturated with moisture Sf b ,°f. Wa ter 
vaporizer at 60° (26 in. mercury), it will contafn 0 01 8 IK e . ntennff , the 
tion to the 0.01 lb. in the alcohol, or 0.023 lb. in alp 3 ^ temp^of 3 77° < F _ 












178 


appendix. 


will vaporize this amount of water and also 0.162 lb. of alcohol, con¬ 
sequently thq smaller amount of alcohol actually used will be suj <. 

lK Under these conditions (total heat of vaporization at 77°F. b <lri S 
458 BTU. per lb.) the heat required for vaporizing is about b y 0 ot tno 
heating value of the alcohol and may be obtained from the exhaust, or 

bv preheating the air used to about 270° F. 

'The best results are obtained by compressing the mixture. to^lSO 
200 lbs. per sq. in., the corresponding max explosion pressure being a 

(vol ^alcohol costs about 15 cents per gal. (2.21 cents Per lb ) 
whenmade from good corn.at 42.4 cents per busheh To compete wit a 
gasoline at 15 cents per gal. its cost must be reduced to 12 cents> P|r ’ 
which : s possible through the use of low-grade grain, cheap \egeta le 
matter, and refuse containing sugar or starch. 




“ “ lb. “ 

Specific gravity. 


* Thermal brake efficiency in per 
cent. 


Gasoline. 

Kerosene. 

Alcohol (90% 
vol.). 

19,000 

18,500 

10,100 

15 

' 13 

15 

2.57 

1.88-. 

2.21 

0.710 

0.8 

0.815 

0.58 

0.725 

0.803 

23. 

18. 

31.7 

11,000 

14,140 

8,030 

1.485 

1.446 

1.758 


Fuei cost per B.H.P. hour (cents) 

Gas-Engine Design. 

Pistons. Max. pressure on piston, P = 0.7854pd 2 . Permissible surface 
pressure, A; = 18 to 22 lbs. per sq. in. (frequently as low as 8 lbs. where 
length of piston is unimportant). Length of piston l>0.llP + dk. Gen¬ 
erally Z = 2 25d to 2.5 d for small en gines ( = 1.25c? to 15 d for large en¬ 
gines)’. Wrist-pin diam. di=Vpd*h =5 680, where h =Total length of 
pin = 0 75d ; bearing length of pin is about 0 5d Thickness of piston 
wall = 6 02d + depth of packing-ring groove+ 0.- in. lo provide for 
expansion the piston is tapered from d at the crank-end to from 0.995d 
to 0.998c? at head end. Pistons over 8 m. in diam. have from 4 to 6 radial 

* Piston-Rings. Radial depth, s = 0.022c?; width, 6 = 0.028d to 0.044c?. 
No. of rings = c? = 56. Space between grooves = 6; depth of groove- 

Cylinders. Thickness of walls for strength, Z = [0 42pd= (/ —p)], where 
f for C.I. may be as high as 3,500 lbs. per sq. in. If d>_4 in., the wall 
may be gradually tapered from t at compression end to 05?. lo allow 
for reboring, etc., 0.16 in. to 0.4 in. should be added to t throughout the 
length. Jacket: where axial forces do not enter into consideration, t\ of 
jacket>0.4 in. If the jacket is cast in one piece with the cylinder, t x = 
0 022(d + 2t) for a test pressure of 420 lbs. per sq. in. (corresponding to 
/ = 8^500 lbs. per sq. in. in a cold test). 

Valves, hi = lift in in.; d 1 = diam. in in.; a x = wdi/ii— area of valve 
opening in sq. in.; a = piston area in sq. in.; S — stroke of piston in ft.; 
c = mean velocity of piston in ft. per sec.; v = mean velocity of gas through 
valve in ft. per sec.; c? = diam. of cyl. in in. Then, ai — ac . v, and, it 
h .< 0 25c?!, ndi} h = ^NS, or = dWS + 1,200. v (mean) =82 ft. per sec. 
Ifl of connecting-rod = 2.55, i>(max.) = 1.6a = 131 ft. per sec. In order 
not to exceed this velocity each position of the piston requires a corre¬ 
sponding lift of the valve, hi > ^5^ = 9,840^, where = sin «(1 ±X cos «), 
« being the angle made by the crank and the direction of center-line of 
piston-rod. 


* Best results obtained. 




















APPENDIX. 


179 


m = 0.5N-Hj = 0.2, 


g % stroke, outward, 

,, % “ return, 

r 

% stroke, outward, 

% “ return, 

t </> = 


2 

5 

10 

20 

98 

95 

90 

80 

.304 

.472 

.648 

.853 

55 

60 

70 

80 

45 

40 

30 

20 

1 00 

.976 

.892 

.759 


30 

40 

45 

5 

70 

60 

55 

5 

.962 

1.011 

1.018 

l.Oi 

90 

95 

98 

100 

10 

5 

2 

0 

554 

394 

.251 

.0 


Thickness of valve in in .-+ 25,600, where d-outside diam of 

?m e 2 in !n"n TO 7 n a ‘ ve -f at -° f sd — 0 32 in Diam of valve-stem - 0.1 21 id 
+ °, 2 m .- to ^ 3 r K m )- ^P n . n g tension on valves: for throttling regulation 

n°7tn S ? on a ih 7 r Ir S ' PCr S V n ' of co, ‘ e surface; for automatic valves, from 
°' 7 ^ wk i P x?/ ! n ; of c ° ne surface, accorrling to speed 
Fiy-^lieeis. Weight of rim in lbs. = 2,165,320fc.fi: (0.75+ />) I H P - 
r_N, where ^-m.e.p on compression stroke-Mn.e.p. on power stroke 
-(h3 usually, fc has the values given on page 74; v = mean vel. of rim 
in ft. per sec., N — r.p.m. and K has the following values: 


One cylinder, single-acting, 

“ double-acting, 

Two cylinders, twin, single-acting, 

single-acting, cranks 180° apart, 
double-acting, tandem or 4 
twin opposing cyls., 


4-cycle. 

1.000 

.615 

.400 

.645 

.085 


2-cycle 

0.400 

.110 

.400 

.085 


Total weight of wheel is about 1.4 times wt. of rim. (The foregoing matter 
has been derived chiefly from Guldner’s 4 Verbrennungsmotoren. ,, ) 

proportion of Parts. It is now customary to assume an explosion 

onn^oVn t! bs -' P er sq 1T } . (m.e.p. =70 lbs.) and a mean piston speed of 
800 850 ft. per mm. For this pressure the values given on pages 99 and 
100 should be altered to the following: 

t of cyl. wall = 0,092 d +0.25 in ; outside diam of cyl-head studs = 
0-29d v ( 1 -v-No. of studs; l of piston = 2.25d; t of rear piston wall = 0.12d- 
wrist-pin: length = 0.47d; diam. = 0.27d; connecting-rod diam at mid-^ 
length = 0.29d; crank-pin: diam. = 0.47rf, length = 0.52d; crank-throws: 
i thickness = 0.3d, width = 0.63d; crank-shaft (at main bearings): diam = 
0.43d, length = 1,12d. 

j Expansion must be allowed for between the jacket and cylinder walls 
(For 144° F. increase in temp., a cyl. 60 in. long will expand 0 053 in in 
length.) 


Large Gas-Engines (over 200 to 300 H.P.) should be double-acting, 
tandem, in order to obtain maximum power with minimum weight. fJune-e’ 
Power, Dec. ’05.) 

Marine Gas-Engine (Otto-Deutz). 4-cyl. horizontal (20-25 H.P per 
cyl.); 275-325 r.p.m.; cylinder: diam. = 10.8 in., length = 33.72 in ; 
stroke = 15.6 in.; crank-pin: length = diam. = 5.4 in.; length of connecting- 
rod = 2.25Xstroke; crank-throws: 6 in. wideX3.7 in. thick; diam. of 
wrist-pin = 2.8 in. 


Gas Turbines. The best results are obtained with high compression, 
rapid introduction of heat (around 900 B.T.U. per lb.), and by an exhaust 
temp, of about 1,300° F. absolute. The charge should be compressed to 
about 570 lbs., maintained at about 140 lbs. in combustion-chamber, and 
exhausted at or below atmospheric pressure. Velocity at nozzle varies 
from 1,600 to 2,600 ft. per sec. according as the temp, of combustion ranges 
from 1,800° to 4,500° F., absolute. For a temp, of 3,600° F. abs. (com¬ 
pression 350 lbs.), the sectional area of combustion-chamber = 100 X sec¬ 
tional area of nozzle, and vol. = sectional areaX5 to 10 times the diam 
Nozzles to resist heat are made of corundum, metal-tipped. Peripheral 
speed of wheels should not exceed 650 ft. per sec. Wheels and vanes 
should be made of nickel steel, which is not weakened or undulv oxidized 
by the temperatures employed. (L. Sekutowicz, Mem. Soc. des Ingenieurs 
Civils, France.) 










180 


APPENDIX. 


Compressed Air. 
Blowers and Compressors. 


For blast-furnaces, 

‘ ‘ Bessemer converters, 

‘ ‘ compressed-air transmission, 

• < “ reservoir storage 


Pressures employed Capacities 

lbs. per sq. in. (gauge), (cu. ft. per min.) 
4 to 10 lbs. Up to 65,000 

15 “ 45 “ “ “ 30,000 

70 “ 115 “ “ “ 10,000 

1,000 and upwards 
2,000 (for torpedo boats) 


For pressures above 75 lbs., two- or three-stage compression should be 
orrJnWed the air passing from compression cylinders into intercoolers 
vUe e t i split up into thin streams and flows over the surfaces of tubes 
Silted by water circulating t hrough them. For two -stage compression. 

nressure in intercooler = V'final pressure to be obtained. For three-stag, 
compression (high p ressures, 1,000 lbs. and’over), pre ssure in first i _ nt e_ 

i _^fin'll r»res • nressure in second intercooler = square of final pres 

employed range from-W0 to 600 f,t per mm 
Blowers for blast-furnaces have strokes of from 3 to 6 ft., and r.p.m up t, 
50 Air and steam cylinders are generally of equal dimensions and hav 
the same length of stroke, pm(air) = r^m(steam). For large, honzonta 
blast-fmnace bowers , = 0.85, for blowers for converters anu compressors 
, = 0.75 to 0.85 (, = mechanical efficiency). 

The volumetric efficiency ranges from 90 to 9o%. “l^y li® 
mined from-the low-pressure cyl. diagram: Volumetric efficiency j e ngt 

of card on atmospheric line + total length between t'nonVoT000 ft'net 
nates of card. Velocity of flow through valves = 3,000 to 5,000 It. per 
min (suction) =5,000 to 7,000 ft per min. (compression). 

IHP =144c’xQ(p — 14 . 7 ) = (0.9X33,000), where c—1.3 to 1.4 for blast¬ 
furnace blowers =1 35 to 1.5 for compressors and blowers for converters, 
O -cu ft of air per'min.; p = absolute pressure of air m lbs per sq. in ; 
0 9 Specific weight of air at 29.52 in. of mercury and at 77° F. compared 
with air at 29.92 in. of mercury and at 3- * . 

Values of x: 


550! 


iVa 


B c 


1 


t 


For p = 

x (poor cooling) = 

x (efficient cooling, compression ac¬ 
cording to pv 1 ' 25 ) = 


25 

81 

50 

.61 

75 

.50 

100 

.44 

125 

.40 

77 

.57 

Ah 

.40 

.35 


Ft.-lbs. of work theoretically required to compress 1 cu. ft. of free air 

P / \ 0 • 29 ”1 

from p to p 1 = (3.44X144p)L0) -1 J (see page 102). 


Rotary Blowers consist of two impeller wheels revolving in a close-fitting 
casing with equal velocities and in opposite directions, the air being drawn 
fn at right angles to the axes of impellers and delivered compressed at 
the opposite opening. The profiles of the impellers are developed m 
the same manner as are the ^eth of gear-wheels ^ . 

Canacitv in cu. ft. per sec., q = XNxB(D- — A) ■ (4 X 30), v here p. . 

B = axial length, and D = diam of impellers, both m feet; 
cross-section of impeller in sq. ft.; ; = volumetric efficiency = 0.6 to 0.9o. 
Mechanical efficiency ranges from 0.45 to 0.85. Pressures from 12 to 80 in. 
of water (0.43 to 2.9 lbs. per sq. in.). 


Mechanical Refrigeration. 


Plate Ice vs. Can Ice. Plate ice does not require the use of distilled 
■water in its production. 1 lb of coal will make about 10 1 is. o p ate 
ice some 275 sq. ft. of freezing surface being required per ton capacity. 

In the manufacture of can ice filtered or distilled water must be used 
otherwise the impurities contained m ordinary water will be retained 
in the core of the block. Can ice does not keep well when stored. 1 lb. 
coal will make from 6 to 7* lbs. of can ice. Plate systems cost from 40 to 

























APPENDIX. 


181 


75% more than can systems. (For 50-ton plant, a can system costs about 
$550 per ton capacity). 


I. Heating and Ventilation. 

Heat Losses due to conduction and radiation, H (in B.T.U.) = Equiva 
lent glass surface, EX(t + 15°), where < = difference between temp, of room 
and outside temp. = 70° F., generally. 

g Exposed wall surface ^ ^ ^ surface I ^ x P os:ec ^ ce] ding or floor sur face 

1 i (Surfaces in sq. ft.) Exposed surfaces are those one side of which is 
subjected to temp, of outside air. 

TiCt 

To H must be added, F = -£^ to provide for ventilation losses, where 

n = No. of changes of air per hour, c = contents of room in cubic ft. The 
total loss (H + V) must be increased 15% for E. exposures and 25% for 
N. and W. exposures. 

Hot-Air Heating. Air should be heated to about 140° F. No. of cu. 
ft. of air heated from 0° to 140° = Q = total heat loss in B.T.U. -5-2.87. 
Assuming that 5 lbs. of coal are burnt per sq. ft, of grate-area per hr., 
and that each lb. supplies 8,000 B.T.U., area of grate in sq. ft. =Q-h 14,000. 
The heating surface of furnace should be from 12 to 20 times the grate 
area, 1 sq. ft. of heating surface giving off about 2,500 B.T.U. per hr. The 
fire-pot should not be less than 12 in. deep, and the cold-air box should 
have an area of about 75% of the combined cross-section of all the pipes. 
For an average outside temp, of 25° F , from 1.75 to 2 lbs. of coal are 
burnt per hr. per sq. ft. of grate area For temp, of —5° F., from 4 to 4.5 
lbs. 

Area of Pipes for Hot-Air Heating. Volume of air in cu. ft per min. 
F = E(t + 15)-5-(60Xl.l). Velocities of air, i> = 280, 400, and 500 ft. per 
min. for 1st, 2d, and 3d floor s respectiv ely. Area of pipes in sq. ft. = V-*-v 

or, diam. of pipe in in. = v 184Fh-v. Area of air outlets should exceed 
l.lXgrate area. Area of registers = 1.25Xarea of pipe supplying same. 
(Condensed from Proceedings Am. Soc. Htg. and Vent. Engrs., W. G. Snow 
and I. P. Bird.) 

Blower System of Heating and Ventilating. In this system the air 
is blown by means of a fan over coils of pipe through which steam cir¬ 
culates. Cu. ft. of air required = Total B.T.U. required-5-55(140 —70), 
where 140 = degs. F. air is to be heated, and 70 = degs. F temp, to which 

rooms are to be heated. The coils are generally of 1-in. pipe, from 200 to 

250 linear ft. of pipe being used per 1,000 cu. ft. of air to be heated per 
min. Air velocities (ft. per min.): Mains, 1,500-2,000; branches to 
register flues, 1,000-1,200; flues to registers, 500-700; from registers, 
300-500. 

Steam Heating, Sizes of Mains for. (Indirect Radiation.) 

Sq. ft. of radiating surface supplied by pipe 100 ft. long = A. 

A = ( 82 + 2.3 p)d- m , where p<16 lbs. (i lb. allowed for drop), 

A = (138 + 2.15p)d 2-61 , “ p> 16 “ (* “ “ “ “ 

For other lengths, multiply by factor c : 

Jj in ft = 50 200 400 600 800 1,000 

c = 1.4 .7 .51 .41 .35 .31 

(p = abs. pressure in lbs. per sq. in.; d = diam. of pipe in in.) 

Diam. of returns, d x = 0.5d when d>7 in. If d<4 in., d l is one size 
smaller; if d = 4 to 7 in., d x = 3£ in 

Direct Radiation: For W.I.-pipe radiators, A will be 20% greater than 
above for a given diam. d, and for C.I. radiators 30% greater. 

[The foregoing has been digested from matter contained in The En¬ 
gineer (Chicago) for Jan. ’06.] 

Compare with: Square feet of radiating surface = lbs. steam per 
min X145 ( = lbs. steam per min. X 60 min. X966 B.T.U. per lb. -5-400 
B.T.U. radiated per sq. ft. per hour). See also formulas on page 70 for 
Flow of Steam in Pipes. 








182 


APPENDIX. 


Cooling of Hot-Water Pipes. Ordinary 2-in. pipes (0.154 in. thick) 
with water at 140° F. cooling to 32° F. (air about 7 F ) lose approxi¬ 
mately as follows: 

0 55 B T.U. per sq. ft per hr. per degree drop in temp (still air). 

1.05 B.T.U. per sq. ft per hr. per degree drop in temp, (air moving I it. 

1 per sq. ft. per hr per degree drop in temp, (in still water at 

39 ° F ) . 

4 5 b.T U. per sq. ft. per hr per degree drop in temp, (in water moving 

lb in. per sec.). 

{Power, Feb. ’06.) 

HYDRAULICS AND HYDRAULIC MACHINERY. 

Plunger-Pumps. Strainer area = (2 to 3 ) X cross-section of suction- 
tube. Area of valve-passages = (1 5 to 2) X cross-section of suction-tube. 

Valves should be of pure rubber. , a _ 

Suction air-chamber vol. = (5 to 10)Xvol of pump cyl. Auction veloc- 
ity = l50 to 200 ft. per min. Vol of pressure air-chamber = (b to S)Xvol. 

Pressure^ velocity = 200 ft. per min. for large pumps and long pipes, = 
300 to 400 ft. per min. for small pumps and short pipes. . , 

Thickness of cyl. wall = 0 . 02 d +0.4 in. for vertical pumps (for horizontal 

Dumps make thickness 25% greater). . ,, 

Thickness of air-chamber walls, * = 0A2pd-e (/< - p), where p-lbs. per 
sq in., gauge, ft (safe) = 2,100 for C. I. =8,500 to 10,000 for W I. 
Efficiencies up to 93%, usually 80 to 85%. 

Centrifugal Pumps. Outer rim velocity in ft. per sec., — 2,7tr\JM . bU, 
relative discharge velocity, do .,=V(l = <j)v- s (v 3 = entering velocity of water). 
<h = r 2 b 2 ^r l b l sin «. (r,, b u and r 2 , b 2 = outer and inner radii of wheels and 

vane widths, respectively; « = angle included between tangent to wheel 
(in direction of motion) and direction of end element of a vane, producedb 
Theoretical pressure height, ^ = (»i 2 +cos a) + o( = 1,3H for short 
conductors and 1.5 H for average lengths). H = total height of delivery = 
suction head -f pressure head. Head against which pump can lilt 
r ,, 2 — r 0 2 ) — 2<7 r,=2r 2 (diam. of suction-tube is made equal to r-j); v 3 — 6 

to 10 ft per sec. No“ of vanes = Z = 6 to 12. Efficiency of best pumps is 

around 80%. Zt \ 

Cu. ft. of water pumped per sec. = ( 2 jrt* 2 —where « x = angle 

between tangent to vane at inner end, and tangent to inner circle of radius 

r 2 : t = thickness of vane in ft. . , ._^ 

Pumping-Engines. Area of valve-seat openings = area ol plungerx 

plunger speed in ft. per min. -e 200. (Chas. A. Hague.) 


SHOP DATA. 


High-Speed Steel Practice (Speeds in ft. per min., cuts in in.). 


Light 


Heavy 


\ 


C I., medium, 

C. I. (hard), tool-steel 
Steel, soft, 

* * hard, 

Mall, iron, 

Brass, 

Chilled iron 


Speed. Cut. 
75 AX* 
35 
150 
92 
100 
120 

3 to 12 ft. per 


Speed. Cut. 

47 bXb 

20 }X£ 

67 *X* 

50 |Xi 

80 AXi 

90 bXb 

in., all cuts. 


The above values for turning sre for diameters of work>6 in.; for 
smaller diams. use speeds 10 to 15% lower. For milling, multiply above 
r.peeds by 1 . 5 ,—for boring, multiply by 0.6 to 0 . 8 . 
















APPENDIX. 


183 


Drilling: Average peripheral speeds (feeds 0 OOS to 0 02 in 
drills > f m ): 


per rev for 


Material, C. I. Steel. 
Speeds, 80 67 


Mall. Iron. Tool Steel. Brass. 
78 33 127 


Reaming: Periph. speed = Periph. speed of drill of same size X2 -h No. of 
re ^mer. heed for reamer = £(drill feed XNo. of reamer lips). 

. Muling. I eriph. speed of cutter for a cut £ in. deep, and a feed of 0.01 
in. per tooth of cutter per rev.: C. I., 90; mall, iron, 86; soft steel, 75; 
tool steel, 37; brass, 140. 

Planing: 50 ft. per min. for steel. (O. M. Becker, Eng. Mag., Aug. ’06.) 


Steel Shafting. 

61 
3.64 
Steel. 

7$X£ i n -> 6 ft. per min. 
6.4 


C. 

150 

2.75 


102 

5.6 


Turning: 

Ft per min., 

Lbs. per min., 

Milling: 

Cut, 

Lbs. per min., 

Drilling: 50 to 100% higher speeds than given above by Becker 
(Results with “A. W.” steel; Engineering, London, 12-15-05.) 


Forged Steel. 

160 32-100 

10 35 

C. I. 

6X1 in., 4 ft. per min. 
5 


Tool. 

Lathe, 

A A 
A t 


Wheel-lathe, 
Planer, 

4 4 

Shaper, 

Drill (11 in.), 
Boring-mill, 


Material. 

C. I., 
Steel, 

4 4 

W. I., 
Steel, 

Cast steel, 
C. I„ 
Brass, 

W. I., 
Steel, 


Ft. per min. 
106 
44 
170 
54 
14 
30 
29 
120 
54 
60 


Lbs. per min. 
2.63 

2.3 to 3.43 
1.69 

4.2 

6 . 

3.2 
18.3 

2.03 

.88 

1.1 


(G. M. Campbell, Am. Mach., 1-25-’06.) 


The average cutting force varies from 100,000 lbs. per sq. in. for soft 
C. I. to 170,000 lbs. for hard C. I. Very hard C. I. may be cut at 25 ft. 
per min.; above 125 ft. per min. for C. I., tools begin to wear rapidly. 
(Univ. of Ill. tests.) 

H.P. Required by Machine Tools = CXlbs. removed per min. C = 
2.5 for hard steel, 2 for W. I., 1.8 for soft steel, and 1.4 for C. I. 

(G. M. Campbell, W. Soc. Eng’rs, Feb. ’06.) 

Standards for Machine Screws. (Threads U. S. form; adopted bv 
the A. S. M. E.) p"— pitch= 1 -f-No. of threads per in.; d— depth= 0.612 

p"; flat at top and bottom= p"-v-8; D=diam. of body of screw. 


Round head 
Flat (counter¬ 
sunk) . 

Flat fillister 

head. 

Oval fillister 
head. 


Thickness of 
Head, t. 
0.7 D 

D- 0.008 
1.739 

1.64D-0.009 0.66D-0.002 
1.64D-0.009 0.66D-0.002 


Diam. of 
Head. 

1.85D-0.005 
2D-0.008 


^-—Slot-„ 

Width. Depth. 

0.173D + 0.015 0.35D + 0.01 

,, ,, D —0.008 

~ 5.217 

“ “ 0.33D-0.001 

“ “ 0.44D —0.001 


Height of oval fillister head= 0.88D — 0.003; radius of oval head=diam. 
of head. Included angle of flat head=82°. 


Diam. in in. 0.060 0.073 0.086 0.099 0.112 0.125 0.138 

Threads per in . . .. 80 72 64 56 48 44 40 

Diam. in in. 0.151 0.164 0.177 0.190 0.216 0.242 0.268 

Threads per in. . . . 36 36 32 30 28 24 22 

Diam. in in. 0.294 0.320 0.346 0.372 0.398 0.424 0.450 

T.ireads per in. . . . 20 20 18 16 16 14 14 


Force Fits. Pressure required in tons = 786< r iZj-r-d 1 .o G , where d = diam. 
of piece, ( = length, 5=allowance for fit, all in inches. (S. H. Moore.) 

















184 


APPENDIX 


/ 


International Metric Threads. Angle of thread = 60°. The top of 
thread is flatted off (i of its height) and , the bottom is rounded to r* 
its height, making total depth of thread — Xthe depth of a sharp V 

thread of same pitch. ._ ___ 

Cost of Electric Power. —In large street-railway power-houses (2,000 
to 10,000 kw. capacity) with coal costing $3.50 per ton, the cost of one 
kilowatt hour at the switchboard is about $0.0078. (C. H. Hile, Power, 

Nov. ’05.) 

Miscellaneous Machine Design. 

Power-Hammers. Lifting force P = weight of hammer W X«, where 
« = i.2 to 2. Lift L = 3 to 6 ft., W = 100 to 2,000 lbs. Velocity = 150 to 
250 ft. per min.; strokes per min. = 20 to 30 

Steam-Hammers. W = 50,000 to 250,000 lbs., « = 1.5 to^ 2^ No. of 

strokes per min. = 72-H\ / L 1 _ Greatest lift L, ,in ft., =0.25\ / W. Diam. 
of piston-rod in in. = 0.055^ W. For small hammers (W = 150 to 2,000 lbs.), 

a = 2 to 3.5. ~ . .. 

Piston-rod diam. in in. = (0.5 to 0.65) Xpiston diam. 

Weight of Anvil and Base W 1 = cLW; (c = 1.8 for iron forging, =3 for 

Ste pressure exerted on anvil = xLW + W u where g = l8 to 25 for iron-work, 
and 25 to 35 for steel. 

Riveters are designed to furnish 100,000 to 200,000 lbs. pressure per 
sq in of rivet section (according to the hardness of rivets), and about 
one-third of this pressure for holding plates together while being riveted. 

Bending Rolls. Diam. of roll d = 2^bt, where 6 = width of plate, and 
t = thickness (d, b, and t in in.). 

Punches. Diam. of punch d\=d, or d — ft; diam. of hole in die = 
(d = diam. of hole in plate, ( = thickness of plate, both in in.). 

Greatest force required = ar.dt. a (or shearing strength of material in 
lbs per sq. in.) = 84,000 to 100,000 for steel plates, =55,000 to 85,000 
for W. I. ( = 17,000 to 28,000 when heated to a dark red), =35,000 to 
55,000 for copper, =13,000 to 20,000 for zinc. Velocity of stroke = 3 to 
4 ft. per min. 

Shears. Vertical clearance of blades = 2°; angle of cutting edge of 
blades = 75° (approx.). Angle included between cutting edges of both 
blades = a = 8° to 10°. Greatest pressure required^when a = 0°)=obt, 
where 5 = width of blade and t = thickness of plate to be sheared. Pressure 

0 225at 2 

required when a>0° = -j—-. Cutting speed = 3 to 6 ft. per min. 

Circular Shears are used for cutting sheets up to 0.2 in. in thickness. 

Diam. of blades = 70 X thickness of sheets to be cut, circumferential 
speed = 100 to 200 ft. per min. 

Rolls for W. I. Diam. of roll in in. d = (t\ — 1 2 ) (1 —cos n), where d is 

obtained from the relation, tan 6 = n. n for W.I. at rolling heat is approx, 
equal to 0 1, whence d= (h — to) X200. (h = thickness of metal before 
rolling, < 2 =thickness after). 

Planers. Speed for tables over 6 ft. wide = 12 to 20 ft. per min.; for 
tables less than 6 ft. wide, from 20 to 28 ft. Return speed = 4 X cutting 
speed. 

Shapers. Cutting speeds up to 48 ft. per min.; return speeds = 4Xcut¬ 
ting speed. 

Belt-Conveyors. Rubber-covered belts from 8 to 60 in. wide running 
on rollers (3 to 5 in. in diam.) are used for conveying grain, coal, ashes, etc., 
where the angle of elevation is not over 23°. 


Spacing of Rollers. 
Driving side. Return side. 

Grain. 6 to 12 ft. 12 to 18 ft 

Coal... 4 to 6 “ • 8 to 12 “ 


For changing direction guide rollers 6 to 8 in. diam. are used; if 
the deviation is abrupt, rollers from 12 to 20 in. diam. are employed. 
The tension of belt is maintained by weights or a screw. 



















APPENDIX. 


185 


Belt Velocities V, in ft. per min.: 

Bran, light grains, etc., 400; heavy grain, 500 to 600. 

Coal (horizontal belt), 460; elevating, 660 to 900. 

Sorting or gathering belts, up to 60. 

Cubic feet moved per hour = 0.0224F(0.96 —2) 2 , where 6 = width of belt 
in in. 

Screw-Conveyors consist of sheet-metal helicoids mounted on hollow 
shafts, with bearings S ft. apart for a 4-in. screw (up to 12 ft. apart for 
an 18-in. screw). Used where elevation angle is less than 30°. 

Troughs of sheet metal 0.08 to 0.16 in. thick; clearance between screw 
and trough = 0.12 to 0.25 in. Spirals of rectangular-section steel bars 
wound edgewise and connected to shaft at about every 20 in. perform 
about 20% less work than screw conveyors. 


Sections of spirals. 
Diam. of trough. 


0 .8X0.2 in. 
4 in. 


1.5X0.28 
8 in. 


2.5X0.28 
12 in. 


3X0.28 
20 in. 


Diam. of screw d<17 in., generally. Pitch of spirals = 0.7d. It.p.m. = 
282 

If 42% of the cross-section of trough is assumed to be filled with the 

material to be moved, then, Cu. ft. moved per hr. = 2.265v'tfs. 

H.P. required = (0.061 to 0.091) XLqr, where L = length of screw in 
ft., g = cu. ft. delivered per sec., and 7- = lbs. per cu. ft. of the material 
moved. 

ELECTROTECHNICS. 

Storage Batteries consist of lead plates immersed in dilute sulphuric 
acid. These plates are either coated with a paste made of red lead (or 
red lead and litharge), or they are cast in the form of grids, the paste 
being forced into the holes of the grids under pressure. The number of 
negative plates is always one more than the number of positive plates. 
The H 2 S0 4 must be pure (free from HN0 3 , HC1, and Sb) and diluted only 
with distilled water, the acid being always poured into the water,—never 
vice versa. The dilute acid or electrolyte should have a sp. g. of about 
1 14 ( = 19° Baume) at the beginning of a charge, which rises to 1.18 to 1 2 
(23° to 25° Baume) at the completion of charge. The density becomes 
altered in use through evaporation of water, loss through ebullition, etc., 
and water or acid should be added from time to time to keep the plates 
covered with % to £ in. of the electrolyte. ‘The sp. g. is the best guide to 
the condition of the cell. Voltage of cell = 2 volts, approx., at beginning 
of charge, rising slowly to 2.2 volts, thence more rapidly to 2.7 volts. 
Discharge begins at about 2 volts, quickly dropping to 1.97 volts, then 
slowly to 1.9 volts and then rapidly to 1.83 volts. If no current is token 
from cell, its voltage is about 2 volts, regardless of the degree to which 
it is charged. Current strength varies (accoikling to size and construc¬ 
tion of cell) from 5.5 to 8.4 amperes per sq. ft. of plate area (charging) 
to 8.4 to 11 amp. per sq. ft. (discharging), or 1.1 to 1.3 amp. per lb. of 
nl a tes 

Capacity is measured by the number of ampere-hours which a cell 
will yield up to a certain defined drop in voltage (7 to 20%) down to 1.83 
volts. The capacity is greater the slower the discharge and varies from 
1.8 to 3.6 amp.-hr. per lb. of plates (rapid discharge) to 5.5 to 7 amp.-hr. 

per lb. (slow discharge). , , ... , . , 

Efficiency:—Good cells yield from 90 to 95% of the amperage with which 
they are charged, and (the voltage of discharge being lower than that ox 
charge) from 75 to 85% of charging energy in watts. 

The first charge must be undertaken as soon as the electrolyte is poured 
into the cells and it should continue until the positive plates have a dark- 
brown color and the so. g. of elect Olyte has risen from 1.14 to at least 
1 18 Time required: from 16 to 50 hours. Charging is generallv accom¬ 
plished with voltages up to 2.4 volts for a steady current, and is interrupted 
when gas bubbles slowly begin to form at about 2.25 volts (i.e , when 
violent ebullition occurs at about 2,5 volts) Cells should be fully charged 
when lying unused, and should be recharged every 10 days or so, if possible 





186 


appendix 




Th« ni-wtrlc Strength of Insulating Materials«-/thickness, 
genemUy (fof para mbbef, strength « thickness). (Approx, values be- 

low.) 

Volts for 

Material. 1 mm. Material. 

thickness. 


Volts for 
1 mm. 
thickness. 


Ordinary paper . 

Fiber and Manila paper. . . 
Presspahn and Impregnated 
paper. 


1.500 
2,200 

4.500 


Varnished paper and linen. 

Ebonite. 

Rubber. 

Gutta-percha. 

Para rubber. 


10.500 

28.500 
21,000 
19,000 

15.500 


(C. Kinzbrunner, Electrician, London, 9-29 and 10 6 ’06.) 


Electro-Magnets, Table for Winding. 


Size of Wire, 

B. & S 

Single- 

covered, 

Turns 

Double- 

covered, 

Turns 

Size of Wire, 

B. & S. 

Single- 

covered, 

Turns 

Double- 

covered, 

Turns 

per 

In. 

per 

Sq. In. 

per 

In. 

per 

Sq. In. 

per 

In. 

per 

Sq. In. 

per 
In. • 

per 

Sq. In. 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 
17 

4.73 

5.29 

5.92 
6.61 
7.55 
8.24 
9.18 

10.44 

11.65 

13. 

14.48 

16.11 

17.92 
19.9 

26.1 

32.7 

40.9 

51. 

64.2 
79.1 

98.3 

127.2 

158.3 
197.1 

244.6 

302.9 

374.7 

461.9 

4.58 

5.11 

5.68 

6.32 

7.18 

7.81 

8.63 

9.88 

11.01 

12.21 

13.5 

14.8 

16.44 

18.26 

24.5 

30.5 
37.7 

46.6 
60.1 
71.2 
86.9 

113.8 

141.4 

173.9 
212.6 

255.5 
315.3 

388.9 

18 

19 

20 
21 
22 

23 

24 

25 

26 

27 

28 

29 

30 

22.08 

25.07 

27.81 

30.81 
34.07 
37.64 
41.49 
45.66 
50.15 
54.95 
60.1 
65.57 
71.27 

568.7 

733.3 

902.2 

1107.6 

1354.3 

1652.8 
2008.2 

2432.4 

2933.8 

3522.9 
4213. 
5016.2 
5926.1 

19.88 

22.8 

25.03 

27.41 

29.98 

32.68 

35.59 

38.6 

41.77 

45.04 

48.45 

51.96 

55.47 

461 .1 

606.5 
730.9 

876.6 

1048.4 

1245.8 
1477.7 
1738.2 

2035.5 

2366.4 

2738.4 

3149.9 

3589.5 


‘Turns per sq in.” are calculated on the assumption that the number 
of layers per in depth = No. of turns per in. (linear) XI. 166 (or 16f% m- 
creaU per in. due to imbedment of layers), and that Turns per sq. in. = 

1 . 166 X (turns per in.) 2 . _ _ . 

No. of feet of wire in 1 cu. in., L = Turns per sq. m.-12. 

Ohms resistance per cu. in.=LXNo. of ohms per linear foot (see table on 

Pa insSon assumed, 8 (diam. of covered wire = diam. of bare wire + 8): 



Size of Wire, 4 to 10 inclusive 

Single-covered, 8 = 0.007 in. 

Double-covered, 8= 0.014 in. 


11 to 18 inclusive 19 and up 
0.005 in. 0.004 in. 

0.010 in. 0.008 in. 


E. M. F. of Dynamos. 


Let 2p = No of poles, 2a = No. of parallel ar- 

N J) 

mature branches into which the current divides; then, E = <Pano——10 s . 

Let a = A-Ml = Pole arc, r = polar pitch), Bi = induction in air-gap D = 
diam. of armature in cm., I = length of armature in cm. Then, kilowatt 
capacity of generator = clND 2 \0 , where c-aBiAlO • 6 . (A No^ of 
ampere-conductors per cm. of circumference, = no/a- 2 ttD, where /a-am¬ 
peres in each conductor) A (ordinarily = 200 ) may reach 300 to 350 
with high Bi, strong saturation of teeth and good ventilation (If a = 0.6 
to 0.85 Bi = 6,000 to 10,000, A = 150 to 200, then c = 1 to 3.) The current 
volume in one slot of an armature ( = / a no) should not exceed 900 amp. 















































APPENDIX. 


187 


If 7a<70 amp., round wire should be used; if >70 amp., conductors 
of rectangular section are preferable. No. of commutator segments = 
0.04no v I a . For no see bottom of page 136. 

Current density in armature conductors: 2 to 5 amp. per sq. mm.( = 400 
to 1,000 cir. mils per amp. = 1,300 to 3,200 amp. per sq. in.). 

Tooth saturation: maximum (at root) = 16,000 to 23,000 lines per sq. 
cm.; minimum (at periphery) = 14,000 to 20,000. 

Saturation of core: 7,000 to 12,000,—lower value for multipolar machines. 

For cooling of armature allow 5 to 10 sq. cm. of external surface for each 
watt wasted. (Kapp.) Brushes: each metal brush should cover from 1 
to 2£ commutator segments (carbon, 2 to 3^). 

Interpoles, Motors and Generators with. Interpoles are used be¬ 
tween the main poles of multipolar machines for the purpose of neutralizing 
the armature magneto-motive force and the reactance voltage due to the 
short-circuiting of the armature coils by the brushes, sparking being thereby 
reduced to a minimum. The higher the speed, the voltage, and the output. 


the greater are 
erators. 

the advantages derived from their 

use. Roughly, for gen- 

K.W. 

Voltage. 

R.P.M. 

Interpoles are: 

750 and up 

250 and up 

1,500 and up 

To be used. 

250 

250 

1,000 

Of slight advantage. 

ft ft * 4 Aft 

100 

250 

1,000 

100 and up 

250-500 

100 

“ no 

400 “ “ 

500 

200 

To be used. 

600 “ “ 

250 

200 

ft ft ft ft ft ft 


In the second and third cases, interpoles are more satisfactory, but they 
increase cost of construction, and good designs are available without 
using them. Interpoles are extensively used in small motors and dynamos 
of high and moderate speeds, but where heating and not sparking is the 
limit of output, their use is attended with increased cost, lowered efficiency, 
and no especial advantages. 

The peripheral speed of commutator should not exceed 115 ft. per sec., 
and commutator should be large enough to radiate the heat generated, 
1 sq. in. of surface being allowed for each 60 amperes of current taken off. 

The leakage or dispersion coefficient is larger than in designs without 
interpoles, being 1.35 for the main magnetic circuits and 1.45 for tne aux¬ 
iliary or interpole circuits. 

To calculate the flux required to enter the armature from the interpoles, 
let A = length of conductor (in cm.) which actually cuts the auxiliary field. 
Then, A = 1.1 X0.7 Xb, where 6 = breadth of pole-shoe (|| to shaft), 1.1 = 
coefficient to allow for “fringing” or spreading of field at the pole-tips, 
and 0.7 = that portion of the length of conductor wffiich is active (i.e., im¬ 
bedded in the armature iron, the remaining 0.3 being taken up by air- 
ducts, insulation, etc.). 

Let S = peripheral speed of armature in cm. per sec., and B = average 
density in the air-gap of interpole in lines per sq. cm. Then, E.M.F. gen¬ 
erated by one conductor = B\S' 10 -8 . As there are two conductors in the 
short-circuited turn, E.M.F. in one turn = 2-BhS’10 —8 , and this must suffice 
to neutralize the reactance voltage. If v = mean reactance voltage [ = re¬ 
actance voltage-*-(?r-f-2)], v = 2B\S' 10~ 8 , whence B, or the desired flux 
density = v‘ 10 s -*-2LS. See pages 140-143. (H. M. Hobart, Elec. Review, 

N. Y„ l-20-’06.) 

Resistance of Iron and Steel Rails. Iron rails have x times the 
resistance of copper conductors of same cross-section and the content of 
manganese in the iron seems to be the chief factor in increasing the value 
of x. For continuous currents, * = 5 + 7 Mn (roughly), where Mn = per 
cent of manganese. A very good rail used in London and containing 
0 19% Mn lias a measured value of #=6.4. (By formula: x = 5+(7X0.19) 
= 6.33.) 




188 


appendix. ' 


Simerheated Steam. The latest and most accurate data on the 
specinc heat of superheated steam at constant Pressure . ^ "Jeh^Im- 
obtained bv Messrs. Knoblauch and Jakob, in 190o, at the Municn ii 
uerial Technical College. They found that at saturation kp rises ' e \ 
Sully with X pressure: but as the temperature rises above that of 
saturation, k v at first rapidly falls reaches a minimum and then rises 
more slowly with further increase in temperature, also that the tempera 
ure giving the minimum becomes greater with greater pressure At 
higher temperatures the specific heats at all pressures apprcmmate each 
other much more closely than at lower temperatures I he following 
table embodies the results obtained by these experimenters. 


Absolute 
Pressure, 
lbs./sq. in. 
28.44 
56.88 
85.32 
113.76 


Specific Heat ( k P ) at 


Satura¬ 

tion. 

0.480 

0.512 

0.548 

0.582 


302° F. 

392° F. 

482° F. 

572° F. 

662° F. 

0.477 

0.510 

0.472 

0.492 

0.513 

0.538 

0.473 

0.483 

0.491 

0.499 

0.478 

0.486 

0.490 

0.494 

0.493 

0.497 

0.500 

0.503 


The mean specific heat through the whole range of temperature from satu- 
ration up to the various pressure-temperature conditions given is as 

follows: 


Gauge 
Pressure. 
50 lbs. 
100 “ 
150 “ 
200 “ 
1250 “ 


300° F. 
0.525 


400° F. 

0.507 

0.560 

0.618 

0.692 


500° F. 

600° F. 

700° F. 

0.497 

0.494 

0.494 

0.528 

0.515 

0.512 

0.560 

0.533 

0.526 

0.585 

0.548 

0.536 

0.625 

0.570 

0.548 


These values have been obtained from diagrams plotted by 
Smith (The Engineer, London, Aug. 23, 0/) from the data of Knoblauch 

and Jakob’s experiments. 

Stresses in Rotating Disks. Let D= outside diam. in ins.; d— 
diam. of hole in ins.; r=rim velocity in ft. per sec ; w= wt. of 1 cu. in. 
of metal used; /,= tensile stress induced by centrifugal force. Then tor 
a plain disk, f t = 4wv 2 ( D 2 + l)d + d 2 ) j gl) 2 . For a solid disk 0), ft- 
Awv 2 -5- g. For a conical disk, ft = 2 wv 2 (D 4 + 3 d — 4Dd a ) gD-{D d) 
For solid conical disk (d=0), f t =2wf+-q. For disks such as are used 
in high-speed steam turbines, and which have logarithmic profiles whose 
equation is y= a log (x-*-b), ft= L5 wv 2 + g when K=.12 wv 2 + g when 

a= ib. (From article by A. M. Levin, Am. Mach., 10-20-04.) 












INDEX 


) 


Absolute temperature, 58 
Acceleration, 43, 71 
Adiabatics, 61 
Admittance, 148 
Air, 100-103 
-chambers, 114 
compressed, 101, 180 
flow of, 101, 161 
-gap, 141 
-lift pump, 114 
-passages, 90 
-pumps, 94, 174, 175 
-space, 141 

Alcohol, denatured, 177 
Algebra, 1 
Alloys, 11, 162 
Alternating currents, 145 
generators for, 148 
Altitudes, 101 
Aluminum, 11, 163 
wires, 156 
Ammonia, 103 
Ampere, 130 

-turns, calculation of, 138 
Angle of torsion, 22 
Angles, pipe, 109 

steel, Carnegie, 34-35 
Annealing, 118 
Anode, 131 
Arc lamps, 159 
Areas of circles, 2 

of plane figures, 5, 162 
Arithmetic, 1 

Arithmetical progression, 4 
Armature, 136 
shafts, 139 
Artificial draft, 93 
Atomic weights, 10 


Bending moment, 23 
and compression, 30 
and tension, 29 
and torsion, 31, 166 
stress, 23 
Bends, pipe, 109 
Bevel gears, 50, 170 
Binomial theorem, 3 
Blacksmith shop, the, 117 
Block and tackle, 45, 171 
Blowers, 102, 180 , 

Boiler accessory apparatus, 93 
dimensions,- 88 
efficiencies, 87 
shell plates, 87 
test, 115 
tubes, 14, 87 
Boilers, steam, 87 
performance of, 87 
proportions, 89 
Bolts, flange-coupling, 22 
dimensions of heads, 120 
strength of, 21-22 
weight of, 15 
Braces and stays, 88 
Brake, Prony, 55 
Brakes, band and friction, 171 
Brass, 11 

Brasses, journal, 47 
Breaking stresses, 19—20 
Brick masonry, 17 
Bridge trusses, 40 
British thermal unit, 57 
Bronzes, 11-12 
Brushes, dynamo, 139 
Building Materials: 

breaking stresses of, 19 
weights of, 12 


Babbitt metal, 11 
Balancing, 85 
Ball bearings, 47, 169 
Barometric condenser, 175 
Batteries, storage, 185 
Beams, deflection of, 26 
I-, Carnegie steel, 32 
of uniform strength, 29 
Bearings, journal, 46, 168 
Belt-conveyors, 128, 184 
Belting, 51 


Calorie, 57 

Calorific values of fuels, 91 
of gases, 96-97 
Capacities of conductors, 159 
Capacity, 130, 147 
Carborundum, 122 
Carnegie structural steel, tables, 
31-36 

Carrying capacity of conductors, 
159 

Case-hardening, 118 


- 189 






190 


INDEX. 


Castings, shrinkage of, 117 
weight of, 117 
Cast-iron columns, 31 
pipe, 13 

properties of, 11 
Cathode, 131 
Cement, 12, 36, 163 
Center of gravity, graphically, 24 
position of, 25, 162 
Center of oscillation, 43 
of pressure, 106 
Centigrade thermometer, 57 
Centrifugal fans. 102 
force, 21; in disks, 188 
force in fly-wheels, 73 
pumps, 113, 182 
Chains, crane, 16 
strength of, 20 
Channels, steel, 33 
Chemical data, 10 
Chimney draft, 92 
gases, 92 

Chimneys, steel, 167 
Chords of circles, 5 
Circles, areas and circumferences of, 
2-3, 5 

Circuits, calculation‘of, 157 
Circular pitch, 49 
Circulating-pumps, 94, 175 
Circumferences of circles, 2-3 
Clearance in cylinders, 63, 75, 97 
Coal, analyses of, 91 
consumption, 85 
-gas, 81 . 

Cocks, 109 

Coefficients of friction, 53 
Collapse, 31, 166 
Collar bearings, 47, 54 
Columns and struts, 30, 165 
Combined stresses, 29—31 
Combustion, 90, 175 
rate of, 93 
Commutator, 139 
Composition of substances, 1C5 
Compound interest, 3 
Compressed-air, 101, 180 
Compression and bendirig, 30 
and torsion, 31 
Compression, steam, 63 
-gas engine, 97 
Compressive stress, 21 
Compressors, air, 180 
Concrete, reinforced, 36 
Condensation, initial, 62 
Condensers, 59, 93 
electrical, 147-148 
Conductance, 131 
Conduction of heat, 56 
Conductors, electrical, 154 
resistance of, 131 
Cone, 8 

Cone pulleys, 52 
Conic frustum, 8 
Conical springs, 23 
Connecting-rod ends, 46, 168 
Connecting-rods, 45, 74, 168, 174 
Continuous beams, 26 


Convection of heat 57 
Conveyors, belt, 128, 184 
Cooling-water, for condensers, 59 
for gas-engines, 97, 161 
Copper, properties of, 11 
Copper wire, tables, 154-155 
Corliss valves, 70, 172 
Corrosion, 95, 176 
Corrugated iron, wt. of, 13 
Cotter-joints, 22 
Cotton-covered wires, 137 
transmission rope, 53 
Coulomb, 130 
Coupling bolts, flange-, 22 
Couplings, 169 
Crane chains, 16 
hooks, 29 

Cranes, electric, 128 
hydraulic, 116 
Crank-arms, 46 

-effort diagrams, 71 
pins, 47, 75 

shafts, 46, 75, 166, 174 
throws, 100, 174 
Cube root, 3 
Cubes of numbers, 2-3 
Cupola, 117 

Currents, electrical, 130 
Cutting speeds of tools, 118-123 
Cycloid, 6 
Cylinder, 8 

Cylinders, gas-engine, 99, 178 
hydraulic, 116 
steam, 66, 174 

Dash-pots, 172 

Dead-center, to place engine on, 
71 

Deflection of beajns, 26 
allowable, 29 ' 

Demagnetization, 141 
Denatured alcohol, 177 
Density of saturated steam, 59 
Diagram factor, 64 
Diagram Zeuner’s valve, 68 
Diameters of engine cylinders, 66 
Diametral pitch, 49 
Dies, 118 

Diesel engine, 82, 99 
Differential pulley, 45 
Direction of currents and lines of 
force, 133 

Disks, stresses in rotating, 188 
Distillates, calorific values of, 92 
Distribution constant, 150 
Divided circuits, 131 
Draft, chimney, 92 
intensity of, 92 
pressures, 92 
-tubes, 112 
Drills, twist, 119 
Driving chain, 51, 170 
Duty of pumping engines, 114 
Dynamometer, 55 

Dynamos, continuous-current, 136, 
186 

design of multipolar, 140 






INDEX. 


191 


Dynamos, efficiencies of 136 
Dyne, 132 

Eccentric loading of columns, 30 
Eccentrics, 46 

Economical steam-engines, 67 
Economizers, 93 
Eddy currents, 137-140 
Efficiency, boiler, 87 
of dynamos, 136 
of gas-engines, 97 
thermal, 61 
Elasticity, 18, 163 
moduli of, 18 
Elbows, 109 

Electric circuits, calculations, 157 
cranes, 128 
currents, 130 
energy, 130 
lighting, 159 
locomotive, 161 
power, 130 
railroading, 160 
traction, 160 
welding, 117 
Electrical units, 130 
Electrolysis, 131 
Electro-magnetism, 132 
Electro-magnets, 134, (table) 186 
Electro-motive force, 130, 186 
Elements of machines, 44 
Elevators, 128 
Ellipse, 5 
Ellipsoid, 8 
Emery wheels, 122 
Energy, 44 # 

Engine proportions, gas-, 99, 178 
steam-, 74 

Engine tests, steam-, 115. 

Engines, steam consumption of, 67 
Entropy, 76 
Epicycloidal teeth, 49 
Evaporation, “from and at’ 212 , 
59 

heat of, 59 

Evaporative condensers, 93 
Expansion, 57 

coefficients of linear, 18 
of gases, 57 
Eye-bars, 21 


Factors of safety, 19 
• Fahrenheit thermometer, 57 
Farad 130 

Faults in indicator cards, 64 
Feeder currents, safe, 160 
Feed-water heating, 93, 175 
Field coils, calculation of, 142 
magnets, 138 
Fire-box plates, 87 
Fits, running, force, shrink, etc., 125, 
183 

Flagging, 13 

Flange-coupling bolts, 22 
Flat plates, strength of, 29 
Floors, loads on. 16 
weight of, 16 


Flow of air, 101, 161 
of steam, 70 
of steam in pipes, 70 
of steam through nozzles 83 
of water in open channels, 109 
of water over weirs, 108 
of water through orifices, 107 
of water through pipes, 109 
Flues, 90 

Flux, magnetic, 132 
Fly-wheels, 21, 73, 75, 100, 164 
Force, 43 

Forgings, allowance in machining, 
118 

Form factor, 150 
Foundations for engines, 100 
Foundry data, 117 
Framed structures, 39 
Frequency, 145 
Friction, 53 

coefficients of, 53 
couplings, 169 
-gearing, 52 
of cup leathers, 116 
of journals, 54 
in ball bearings, 48 
in water pipes, 108 
locomotive, 85 
Fuels, 91, 92, 97 
Furnaces, 90 
Fuses, 159 
Fusible plugs, 94 
Fusing points, 11, 12 

Galvanized-iron wire, 16 
-steel wire, 16 
Gap machine frames, 167 
Gas, coal-, London, 81 
-engine data, 80, 161 
-engine design, 99, 178 
fuels, 92, 175 
-pipe, 13 

Gas producers, 176 
Gas turbines, 179 
Gases, weights of, 10 
Gauss, 132 
Gay-Lussac’s law, 58 
Gearing, 48 
train of, 45 

Gears, proportions of, 51 
Geometrical progression, 4 
Gilbert, 132 
Glass, 12, 13 
Gordon’s formulas, 30 
Governors, 68 
Graphite, 55 
Grate area, 85 
Gravity, center of, 24-25 
force of, 43 
Grinding wheels 122 
Grindstones, 122 
Grooving, 95 
Gun-metal 11 
Gyration, radius of 24 

Hammers, 184 
Hardness of materials. 19 






192 


INDEX. 


V 


Haulage rope, 16 <■ 

Head, 107 

Heat, 56 K 

latent, 58 
sensible, 59 
total, 59 
-units, 57 

Heating of conductors, 159 
and ventilation, 104, 181 
surface, 85-87 
Helical springs, 22, 164 
Henry, 147 

High-speed tool steel, 122, 182 
twist-drills, 125 
Hoisting-engines, 128 
speeds, 116 

Horse-power, calculation of, 64, 97, 
173 

of boilers, 87; metric, 162 
of locomotives, 84 
Hot-air heating, 181 
Hydraulic cylinders, 116 
crane, 116 
gradient, 109 
pipe, riveted, 13 
power transmission, 116 
ram, 114 
Hydraulics, 106 
Hydrostatic pressure, 106 
Hyperbola, 8 
Hyperbolic logarithms, 66 
Hysteresis, 133, 140 

I-beams, steel, tables of, 32 
Illumination, 160 
Impact, 43 
Impedance, 146, 148 
Incandescent lamps, 160 
Inclined plane, 45 
Incrustation, 95, 176 
Indicated horse-power, 64 
Indicator diagrams, 63-65 
Inductance, 146, 158 
Inertia diagrams, 71 
moment of, 23-24 
Initial condensation, 62-63 
Injectors, 94 

Insulation, armature, 137 
dielectric strength of, 186 
resistance, 159 
Intensity of draft, 92 
of magnetic field, 132 
Interest, compound, 3 
Internal-combustion engines, 95, 
176 

entrony diagrams for, 79 
Interpolation, 4 
Interpoles, 187 
Involute teeth, 49 
Iron, cast- and wrought-, 11 
wire, 15 
Isothermals, 61 

Jackets, steam, 62, 63 
Jet condensers, 93 
Joule, 130 
Joule’s law, 131 


Journals, 46, 168 
friction of, 54 

Iveys, strength of, 22 
Kinetic energy, 44 
of steam, 83 
Kirchoff’s laws, 131 

Lacing, 52 
Lag-screws, 15 
Laminated springs, 29, 165 
Lap, steam, 68 
Latent heat, 58 
Lead of valves, 68 
Lead pipe, 14 

Leakage factor (magnetism), 141 
steam-, 63-64 
Leather belts, 51 
Lever, 44 

Lifting power of magnets, 134 
Lines of force, 132 
Loam, 117 

Locomotives, electric, 161 
steam, 84, 175 

Logarithms, common, 4; table 6 
hyperbolic, 66 
Lubrication, 54 


Machine design, proportioning a se-r 
nes of machines, 128 
miscellaneous, 184 
-screws, 119, 183 
shop, the, 118 

Machinery, power required for, 126 
Machines, elements of, 44 
Magnetic circuit, 133 
densities in transformers, 153 
field, intensity of, 132 
flux, 132 
induction, 134L-, 

Magnetizing force, intensity of, 132 
Magneto-motive force, 132 
Magnets, electro-, 134 
field-, 138 
Malleable iron, 163 
Manila rope, 53 
Marine engines, 173 
Marriotte’s law, 57 
Masonry, brick, 17 
Mass, 43 
Materials, 11 
boiler, 11 

hardness of, relative, 19 
strength of, 18 
Mathematics, 1 
Maxwell, 134 

Mean spherical candle-power, 160 
Measures, English and metric, 1 10 
Mechanical refrigeration, 102 
stoking, 93, 176 
Mensuration, 5 
Metal-cutting saws, 125 ' 

Metals, 11 , 162 

Metric screw-threads, 119 , 184 
, r ^'eights and measures, 1, 162 
Milling cutters, 118 
Moduli of elasticity, 18 







INDEX, 


193 


Modulus section, 23 
of rupture, 31 
Moisture in steam, 58 
Moment of inertia, 23, 24, 26, 165 
of resistance, 23 
Momentum, 43 
Monocyclic generator, 150 
Morse tapers, 119 
Motors, continuous-current, 143 
for machine-tools, 127 
Multiple-expansion diagrams, 66 
Multipolar dynamos, design of, 140 

Nails, holding power of, 16 
wire, 15 

Nernst lamp, 160 
Neutral axis, 23 

Nozzles, flow of steam through, 83 
Nuts, number in 100 lbs., 15 
proportions of, 120 

Oersted, 132 
Ohm, 130 
Ohm’s law, 131 
Overshot wheels, 111 

Paint and painting, 129 
Parabola, 5 
Paraboloid, 8 
Pedestals, 168 
Pelton wheel. 111 
Pendulum, 43 
Performance of boilers, 87 
of pumping plant, 115 
Periodicity, 145 
Permeability, 132 
Petroleum, calorific value of, 92 
Phase, 145 
Pins, 22 

Pipe, cast-iron, weight of, 13 
lead, 4 

strength of, 20 
threads on wrought-iron, 14 
Pipes, steam, 94 
Piston rings, 168, 178 
-rods, 74, 168, 174 
speeds, 70, 97, 173 
-valves, 85 

Pistons, 74, 100, 174, 178 
Pivots, 47, 54 
Planers, 184 
Plates, boiler-shell, 87 
flat, 29 

Plunger electro-magnets, 134 
pumps, 114, 182 
Pneumatic tools, 102 
Poisson’s ratio, 18 
Polar moment of inertia, 24 
Potential energy, 44 
Power, 44 

cost of, 127, 184 
-factor, 146, 157 
for shafting, 127 
hammers, 44, 184 
measurement of, 55 
plants, cost of, 127 


Power required by cutting tools, 125 
. “ machinery, 126, 183 

transmission, hydraulic, 116 

_ . . “ electric, 157 

Priming, 95 
Producers, gas, 176 
Prony brake, 55 
Pulley blocks, 171 
Pulleys, 45, 52, 170 
cone, 52 
Pulsometer, 114 
Pumping engines, 114, 182 
Pumps, air, 94 

centrifugal, 113, 182 
circulating, 94 
plunger, 114, 182 
Punches and dies, 118, 184 
Pyramid, 8; frustum of, 8 
Pyrometers, 57 

Quantity of electricity, 130 
Quarter-phase generator, 149 

Radiation of heat, 56, 105 
Radius of gyration, 24 
Rails, elevation of, 175 
resistance of, 160, 187 
Ram, hydraulic, 114 
Rate of combustion, 93 
Ratio of expansion, 63, 66 
Rawhide gears, 50 
Reactance, 146 
voltage, 143 
Receiver volume, 75 
Recoil, 44 
Re-evaporation, 63 
Refrigeration, mechanical, 102, 180 
Reheating of air, 102 
Reinforced concrete, 36, 166 
Reluctance, 132 
Reluctivity, 133 
Renold chain gear, 51 
Resilience, 18 
Resistance, 130 
of conductors, 131, 155 
of rails, 160, 187 
specific, 131 
train, 84, 160 
Resonance, 148 
Rheostats, 144 
Rings, strength of, 165 
Riveted hydraulic pipe, 13 
joints, 21, 161, 164 
Riveting, 22 
Rivets, boiler, 88, 161 
bridge, weight of, 15 
proportions of, 21 
Roller bearings, 47, 54, 169 
Rolls, 184 
Roof loads, 17 
trusses, 41 

Roofing materials, 13 
slate, 13 

Rope, haulage, 16 
manila, 53 
strength of, 20 
transmission, 16, 53 







194 


INDEX 


Rope, wire hoisting-, 16 
Rubber belts, 51 
Rupture, modulus of, 31 

Safety, factor of, 19, 22 
-valve, 45, 94 
Sand,117 

Saturated steam, 58-60, 172 
Saws, metal-cutting circular, 125 
Scale, 95 
Screw, 45 

conveyors, 185 
-propeller, 173 
-threads, 119-120, 184 
Screws, power transmission, 168 
machine, 119 
Section modulus, 23 
Sector of circle, 5 
Segment of circle, 5 
of sphere, 8 

Self-induction, 137, 146 
Sensible heat, 59 
Serve tubes, 86 
Shaft-couplings, 47 
Shafting, 46 

power absorbed by, 127 
Shafts, armature, 139 
stiffness of, 22 
strength of, 22 
Shapers, 184 
Shear legs, 42 
stress, 21-28 
Shears, 184 

Sheet-metal gauges, 121 
Shingles, pine, 13 
Shop data, 117 
Shrink fits, 125 
Shrinkage of castings, 117 
Simpson’s rule, 6 
Single-phase generator, 148 
Sinking fund, 4 
Siphon condenser, 175 
Skylight and floor glass, 13 
Slate, 12, 13 
Solenoid, 136 
Space factor, 142 
Sparking, 137. 

Specific gravities of substances, 11,12 
heat, 57, 104 
heats of a gas, 60 
inductive capacity, 147 
resistance, 131 
volume of steam, 61 
Spikes, 15 

Spiral gears, 50, 170 
springs, 23 
Snlines, 22 

Springs, laminated, 29 
strength of, 23 
Spur gears, 49 
Square root, 3 
Squares of numbers, 2 
Stay-bolts, 88 
Stayed surfaces, 29 
Steam boilers, 87, 89 

consumption by engines, 67, 172 
-engine proportions, 74, 174 


Steam-flow, 70, 83 
hammers, 184 
-heating, 105, 181 
jackets, 62, 63 
moisture in, 58 
-pipe coverings, 56 
pipes, 75, 94, 105 
ports, 75 
saturated, 58-60 
superheated, 58, 61-62, 67 
turbines, 82 

Steel, properties of, 11, 162 
Carnegie structural, 31-36 
Steels, alloy, properties of, 11 
Stiffness of shafts, 22 
Stones, weights of various, 12 
Storage batteries, 185 
Strain, 18 
Stray-field, 138 
Strength of bolts, 21 
of chain, 20 

of cotter-joints, 22, 164 
of crane-hooks, 29 
of cylinders, 20, 164 
of eye-bars, 21 
of flange-coupling bolts, 22 
of flat plates, 29 
of gear teeth, 50 
of helical springs, 22 
of laminated springs, 29 
of materials, 18, 163 
of pipes, 20 
of riveted joints, 21 
of ropes, 20 
of shafts, 22 
of stayed surfaces, 29 
Stress, 18 
bending, 23 
compressive^ 21 

diagrams for framed structures, 39 
due to impulsive load, 18 
heat-, 18 
shear, 21-28 
tensile, 20 
torsional, 22 
Stresses, breaking, 20 
allowable, 163 
combined, 29 
Structural steel, 31-36 
Stuffing boxes, 168 
Superheated steam, 58, 61, 62, 67, 
172, 188 

Superheater surface, 62 
Surface-condensers, 93, 174 
Surfaces of solids, 7 
Susceptibility, 132 

T-shapes, Carnegie steel, 34 
Tantalum lamp, 160 
Tap drills, 119-120 
Tapers, Morse, 119 
turning, 119 
Temper, 11 
Temperature, 57 

-entropy diagrams, 76 
Tempering, 118 
I Tensile stress, 20 



INDEX 


195 


Tension and bending, 29 
Thermal efficiency, 61 
Thermometers, 57 
Threads, pipe (wrought-iron), 14 
screw-, 119-120 
Three-phase generator, 150 
Thrust bearings, 46, 168 
Tin, 11 
Tin plate, 13 

Tool steel, high-speed, 122, 182 
Tooth density (magnetic), 140 
Torque, 144 
Torsion, angle of, 22 
and bending, 166 
and compression, 31 
Torsional stress, 22 
Total heat, 59 

Traction of electro-magnets, 134 
Tractive force, 160 
power, 84 

Train resistance, 84, 160 
Transformers, 151 
design of, 151 

Transmission circuits (electric), 157 
rope, 16 
Trapezoid, 5 

Trigonometry, with table, 8, 9 
Trusses, 40 
Tubes, boiler, 14, 88 
holding power of 87 
Turbines, gas, 179 
hydraulic, 111 
steam, 82 
Twist-drills, 119 
high-speed, 125 

Undershot wheels, 110 

Vacuum, 64 
Valve-stems, 46 
Valves, engine, 68 
gate-, 109 

proportions of, 70, 178 
Velocity, 43 
Ventilation, 104 


Volt, 130 

Volumes of solids, 7 

Water, 106 

consumption, 64 
pipe, 13 
wheels, 110 
Watt, 130 
Wedge, 45 
Weight of bolts, 15 
of bars, 12 

of building materials, 12, 13 
of flat wrought-iron bars, 13 
of gases, 10 
of plates, 12 
of rivets, 15 
of rods, 12 

of round wrought-iron bars, 12 
of sheet-metals, 13 
of spheres, 12 

of square wrought-iron bars, 12 
of tubes, 12 
of woods, 12 
Weights and measures 1 
Welding, 117 
Wheel and axle, 45 
Winding table for magnets 186 
Wire, galvanized-iron, 16 
galvanized-steel strand, 16 
gauges, 121 
hoisting rope, 16 
iron, 15 
nails, 15 
rope, 16, 53 
steel, 15 

Wiring formulas, 156 
Wood, calorific value of, 92 
Woods, weight of, 12 
Work, 18 

Worm gearing, 50, 170 
Wrought-iron pipe, 14 
properties of, 11 

Z-bars, Carnegie steel, 35 
Zeuner’s diagram, 68 
Zinc, 11 



















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